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Alcune considerazioni sui metodi iterativi per la risoluzione di sistemi lineari. Tesi di laurea / laureanda M. R. Cagnazzo ; relat. L. Guercia
| Alcune considerazioni sui metodi iterativi per la risoluzione di sistemi lineari. Tesi di laurea / laureanda M. R. Cagnazzo ; relat. L. Guercia |
| Autore | Cagnazzo, Maria Rosaria |
| Pubbl/distr/stampa | Lecce : Università degli studi. Facoltà di Scienze. Corso di laurea in Matematica, a.a. 1991-92 |
| Altri autori (Persone) | Guercia, Liana |
| Soggetto topico |
Iterative methods
Linear systems |
| Classificazione | AMS 65F10 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Record Nr. | UNISALENTO-991000649189707536 |
Cagnazzo, Maria Rosaria
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| Lecce : Università degli studi. Facoltà di Scienze. Corso di laurea in Matematica, a.a. 1991-92 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Assessment of data by a second-order transfer function / / D. G. Camell
| Assessment of data by a second-order transfer function / / D. G. Camell |
| Autore | Camell Dennis G |
| Pubbl/distr/stampa | Gaithersburg, MD : , : U.S. Dept. of Commerce, National Institute of Standards and Technology, , 1994 |
| Descrizione fisica | 1 online resource |
| Altri autori (Persone) | CamellDennis G |
| Collana | NIST technical note |
| Soggetto topico |
Electromagnetic pulse
Linear systems Transfer functions |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910711209103321 |
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Camell Dennis G
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| Gaithersburg, MD : , : U.S. Dept. of Commerce, National Institute of Standards and Technology, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Bayes linear statistics [[electronic resource] ] : theory and methods / / Michael Goldstein and David Wooff
| Bayes linear statistics [[electronic resource] ] : theory and methods / / Michael Goldstein and David Wooff |
| Autore | Goldstein Michael <1949-> |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina |
519.5
519.542 |
| Altri autori (Persone) | WooffDavid |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Bayesian statistical decision theory
Linear systems Computational complexity |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-85495-2
9786610854950 0-470-06566-4 0-470-06567-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Bayes Linear Statistics; Contents; Preface; 1 The Bayes linear approach; 1.1 Combining beliefs with data; 1.2 The Bayesian approach; 1.3 Features of the Bayes linear approach; 1.4 Example; 1.4.1 Expectation, variance, and standardization; 1.4.2 Prior inputs; 1.4.3 Adjusted expectations; 1.4.4 Adjusted versions; 1.4.5 Adjusted variances; 1.4.6 Checking data inputs; 1.4.7 Observed adjusted expectations; 1.4.8 Diagnostics for adjusted beliefs; 1.4.9 Further diagnostics for the adjusted versions; 1.4.10 Summary of basic adjustment; 1.4.11 Diagnostics for collections
1.4.12 Exploring collections of beliefs via canonical structure1.4.13 Modifying the original specifications; 1.4.14 Repeating the analysis for the revised model; 1.4.15 Global analysis of collections of observations; 1.4.16 Partial adjustments; 1.4.17 Partial diagnostics; 1.4.18 Summary; 1.5 Overview; 2 Expectation; 2.1 Expectation as a primitive; 2.2 Discussion: expectation as a primitive; 2.3 Quantifying collections of uncertainties; 2.4 Specifying prior beliefs; 2.4.1 Example: oral glucose tolerance test; 2.5 Qualitative and quantitative prior specification 2.6 Example: qualitative representation of uncertainty2.6.1 Identifying the quantities of interest; 2.6.2 Identifying relevant prior information; 2.6.3 Sources of variation; 2.6.4 Representing population variation; 2.6.5 The qualitative representation; 2.6.6 Graphical models; 2.7 Example: quantifying uncertainty; 2.7.1 Prior expectations; 2.7.2 Prior variances; 2.7.3 Prior covariances; 2.7.4 Summary of belief specifications; 2.8 Discussion: on the various methods for assigning expectations; 3 Adjusting beliefs; 3.1 Adjusted expectation; 3.2 Properties of adjusted expectation 3.3 Adjusted variance3.4 Interpretations of belief adjustment; 3.5 Foundational issues concerning belief adjustment; 3.6 Example: one-dimensional problem; 3.7 Collections of adjusted beliefs; 3.8 Examples; 3.8.1 Algebraic example; 3.8.2 Oral glucose tolerance test; 3.8.3 Many oral glucose tolerance tests; 3.9 Canonical analysis for a belief adjustment; 3.9.1 Canonical directions for the adjustment; 3.9.2 The resolution transform; 3.9.3 Partitioning the resolution; 3.9.4 The reverse adjustment; 3.9.5 Minimal linear sufficiency; 3.9.6 The adjusted belief transform matrix 3.10 The geometric interpretation of belief adjustment3.11 Examples; 3.11.1 Simple one-dimensional problem; 3.11.2 Algebraic example; 3.11.3 Oral glucose tolerance test; 3.12 Further reading; 4 The observed adjustment; 4.1 Discrepancy; 4.1.1 Discrepancy for a collection; 4.1.2 Evaluating discrepancy over a basis; 4.1.3 Discrepancy for quantities with variance zero; 4.2 Properties of discrepancy measures; 4.2.1 Evaluating the discrepancy vector over a basis; 4.3 Examples; 4.3.1 Simple one-dimensional problem; 4.3.2 Detecting degeneracy; 4.3.3 Oral glucose tolerance test 4.4 The observed adjustment |
| Record Nr. | UNINA-9910143714703321 |
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Goldstein Michael <1949->
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| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Bayes linear statistics [[electronic resource] ] : theory and methods / / Michael Goldstein and David Wooff
| Bayes linear statistics [[electronic resource] ] : theory and methods / / Michael Goldstein and David Wooff |
| Autore | Goldstein Michael <1949-> |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina |
519.5
519.542 |
| Altri autori (Persone) | WooffDavid |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Bayesian statistical decision theory
Linear systems Computational complexity |
| ISBN |
1-280-85495-2
9786610854950 0-470-06566-4 0-470-06567-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Bayes Linear Statistics; Contents; Preface; 1 The Bayes linear approach; 1.1 Combining beliefs with data; 1.2 The Bayesian approach; 1.3 Features of the Bayes linear approach; 1.4 Example; 1.4.1 Expectation, variance, and standardization; 1.4.2 Prior inputs; 1.4.3 Adjusted expectations; 1.4.4 Adjusted versions; 1.4.5 Adjusted variances; 1.4.6 Checking data inputs; 1.4.7 Observed adjusted expectations; 1.4.8 Diagnostics for adjusted beliefs; 1.4.9 Further diagnostics for the adjusted versions; 1.4.10 Summary of basic adjustment; 1.4.11 Diagnostics for collections
1.4.12 Exploring collections of beliefs via canonical structure1.4.13 Modifying the original specifications; 1.4.14 Repeating the analysis for the revised model; 1.4.15 Global analysis of collections of observations; 1.4.16 Partial adjustments; 1.4.17 Partial diagnostics; 1.4.18 Summary; 1.5 Overview; 2 Expectation; 2.1 Expectation as a primitive; 2.2 Discussion: expectation as a primitive; 2.3 Quantifying collections of uncertainties; 2.4 Specifying prior beliefs; 2.4.1 Example: oral glucose tolerance test; 2.5 Qualitative and quantitative prior specification 2.6 Example: qualitative representation of uncertainty2.6.1 Identifying the quantities of interest; 2.6.2 Identifying relevant prior information; 2.6.3 Sources of variation; 2.6.4 Representing population variation; 2.6.5 The qualitative representation; 2.6.6 Graphical models; 2.7 Example: quantifying uncertainty; 2.7.1 Prior expectations; 2.7.2 Prior variances; 2.7.3 Prior covariances; 2.7.4 Summary of belief specifications; 2.8 Discussion: on the various methods for assigning expectations; 3 Adjusting beliefs; 3.1 Adjusted expectation; 3.2 Properties of adjusted expectation 3.3 Adjusted variance3.4 Interpretations of belief adjustment; 3.5 Foundational issues concerning belief adjustment; 3.6 Example: one-dimensional problem; 3.7 Collections of adjusted beliefs; 3.8 Examples; 3.8.1 Algebraic example; 3.8.2 Oral glucose tolerance test; 3.8.3 Many oral glucose tolerance tests; 3.9 Canonical analysis for a belief adjustment; 3.9.1 Canonical directions for the adjustment; 3.9.2 The resolution transform; 3.9.3 Partitioning the resolution; 3.9.4 The reverse adjustment; 3.9.5 Minimal linear sufficiency; 3.9.6 The adjusted belief transform matrix 3.10 The geometric interpretation of belief adjustment3.11 Examples; 3.11.1 Simple one-dimensional problem; 3.11.2 Algebraic example; 3.11.3 Oral glucose tolerance test; 3.12 Further reading; 4 The observed adjustment; 4.1 Discrepancy; 4.1.1 Discrepancy for a collection; 4.1.2 Evaluating discrepancy over a basis; 4.1.3 Discrepancy for quantities with variance zero; 4.2 Properties of discrepancy measures; 4.2.1 Evaluating the discrepancy vector over a basis; 4.3 Examples; 4.3.1 Simple one-dimensional problem; 4.3.2 Detecting degeneracy; 4.3.3 Oral glucose tolerance test 4.4 The observed adjustment |
| Record Nr. | UNINA-9910830430903321 |
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Goldstein Michael <1949->
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| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Bayes linear statistics : theory and methods / / Michael Goldstein and David Wooff
| Bayes linear statistics : theory and methods / / Michael Goldstein and David Wooff |
| Autore | Goldstein Michael <1949-> |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina | 519.5/42 |
| Altri autori (Persone) | WooffDavid |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Bayesian statistical decision theory
Linear systems Computational complexity |
| ISBN |
1-280-85495-2
9786610854950 0-470-06566-4 0-470-06567-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Bayes Linear Statistics; Contents; Preface; 1 The Bayes linear approach; 1.1 Combining beliefs with data; 1.2 The Bayesian approach; 1.3 Features of the Bayes linear approach; 1.4 Example; 1.4.1 Expectation, variance, and standardization; 1.4.2 Prior inputs; 1.4.3 Adjusted expectations; 1.4.4 Adjusted versions; 1.4.5 Adjusted variances; 1.4.6 Checking data inputs; 1.4.7 Observed adjusted expectations; 1.4.8 Diagnostics for adjusted beliefs; 1.4.9 Further diagnostics for the adjusted versions; 1.4.10 Summary of basic adjustment; 1.4.11 Diagnostics for collections
1.4.12 Exploring collections of beliefs via canonical structure1.4.13 Modifying the original specifications; 1.4.14 Repeating the analysis for the revised model; 1.4.15 Global analysis of collections of observations; 1.4.16 Partial adjustments; 1.4.17 Partial diagnostics; 1.4.18 Summary; 1.5 Overview; 2 Expectation; 2.1 Expectation as a primitive; 2.2 Discussion: expectation as a primitive; 2.3 Quantifying collections of uncertainties; 2.4 Specifying prior beliefs; 2.4.1 Example: oral glucose tolerance test; 2.5 Qualitative and quantitative prior specification 2.6 Example: qualitative representation of uncertainty2.6.1 Identifying the quantities of interest; 2.6.2 Identifying relevant prior information; 2.6.3 Sources of variation; 2.6.4 Representing population variation; 2.6.5 The qualitative representation; 2.6.6 Graphical models; 2.7 Example: quantifying uncertainty; 2.7.1 Prior expectations; 2.7.2 Prior variances; 2.7.3 Prior covariances; 2.7.4 Summary of belief specifications; 2.8 Discussion: on the various methods for assigning expectations; 3 Adjusting beliefs; 3.1 Adjusted expectation; 3.2 Properties of adjusted expectation 3.3 Adjusted variance3.4 Interpretations of belief adjustment; 3.5 Foundational issues concerning belief adjustment; 3.6 Example: one-dimensional problem; 3.7 Collections of adjusted beliefs; 3.8 Examples; 3.8.1 Algebraic example; 3.8.2 Oral glucose tolerance test; 3.8.3 Many oral glucose tolerance tests; 3.9 Canonical analysis for a belief adjustment; 3.9.1 Canonical directions for the adjustment; 3.9.2 The resolution transform; 3.9.3 Partitioning the resolution; 3.9.4 The reverse adjustment; 3.9.5 Minimal linear sufficiency; 3.9.6 The adjusted belief transform matrix 3.10 The geometric interpretation of belief adjustment3.11 Examples; 3.11.1 Simple one-dimensional problem; 3.11.2 Algebraic example; 3.11.3 Oral glucose tolerance test; 3.12 Further reading; 4 The observed adjustment; 4.1 Discrepancy; 4.1.1 Discrepancy for a collection; 4.1.2 Evaluating discrepancy over a basis; 4.1.3 Discrepancy for quantities with variance zero; 4.2 Properties of discrepancy measures; 4.2.1 Evaluating the discrepancy vector over a basis; 4.3 Examples; 4.3.1 Simple one-dimensional problem; 4.3.2 Detecting degeneracy; 4.3.3 Oral glucose tolerance test 4.4 The observed adjustment |
| Record Nr. | UNINA-9910876938403321 |
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Goldstein Michael <1949->
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| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Combinatorial matrix theory and generalized inverses of matrices / / Ravindra B. Bapat ... [et al.], editors
| Combinatorial matrix theory and generalized inverses of matrices / / Ravindra B. Bapat ... [et al.], editors |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New Delhi ; ; New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (xvii, 277 pages) : illustrations (some color) |
| Disciplina | 512.9/434 |
| Collana | Gale eBooks |
| Soggetto topico |
Matrices
Linear systems |
| ISBN |
1-299-33685-X
81-322-1053-0 |
| Classificazione | 58-0258J0558J2019K5615-0615A0915Bxx |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube -- Notes on Explicit Block Diagonalization -- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs -- Matrix Product of Graphs -- Determinant of the Laplacian Matrix of Weighted Directed Graphs -- From Multivariate Skewed Distributions to Copulas -- Revisiting the BLUE in a Linear Model via Proper Eigenvectors -- Inference in Error Orthogonal Models -- On the Entries of Orthogonal Projection Matrices -- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces -- The Reverse Order Law in Indefinite Inner Product Spaces -- Generalized Inverses and Approximation Numbers -- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space -- Products and Sums of Idempotent Matrices over Principal Ideal Domain -- Perfect Semiring of Nonnegative Matrices -- Regular Matrices over an Incline -- Matrix Partial Orders associated with Space Preorder -- An Illustrated Introduction to Some Old Magic Squares from India -- Appendix: Report on CMTGIM 2012, Manipal -- Index. |
| Record Nr. | UNINA-9910741158303321 |
| New Delhi ; ; New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Consensus over switching network topology : characterizing system parameters and joint connectivity / / Jiahu Qin [et al.]
| Consensus over switching network topology : characterizing system parameters and joint connectivity / / Jiahu Qin [et al.] |
| Autore | Qin Jiahu |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (254 pages) |
| Disciplina | 006.30285436 |
| Collana | Studies in Systems, Decision and Control |
| Soggetto topico |
Multiagent systems
Linear systems Topology |
| ISBN | 3-030-85657-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Background -- 1.2 Outline and Overview of the Chapters -- 1.3 Preliminary -- 1.3.1 Digraph and Matrix -- 1.3.2 Dynamically Changing Digraph -- 1.3.3 Nonnegative Matrix and M-Matrix Theory -- 1.3.4 Kronecker Product -- 1.3.5 Notations -- 2 Consensus of Double-Integrators over Switching Network Topology -- 2.1 Continuous-Time Systems with Piecewise Fixed Network Topology -- 2.1.1 Agent Model Without/with Communication Delay -- 2.1.2 Stationary Consensus without Communication Delay -- 2.1.3 Stationary Consensus with Communication Delay -- 2.1.4 Numerical Examples -- 2.1.5 Conclusion -- 2.1.6 Appendix -- 2.2 Sampled-Data Systems with Piecewise Continuous Network Topology -- 2.2.1 Sampled-Data Agent Model with Nonuniform and Time-Varying Communication Delays -- 2.2.2 Graph Augmentation and Joint Connectivity -- 2.2.3 Consensus via Product of Stochastic Matrices -- 2.2.4 Numerical Examples -- 2.2.5 Conclusion -- 2.2.6 Appendix -- 2.3 Asynchronous Update Systems with Piecewise Continuous Network Topology -- 2.3.1 Asynchronous Update Agent Model -- 2.3.2 Consensus for Asynchronous Update -- 2.3.3 Consensus Analysis via Augmented Synchronous Update -- 2.3.4 Numerical Examples -- 2.3.5 Conclusion -- 3 Generic Linear Systems over Undirected Network: Controllability and Connectivity -- 3.1 Piecewise Continuous and Balanced Network Topology -- 3.1.1 Network Configuration -- 3.1.2 Weakly Connected Network Topology (WCNT) -- 3.1.3 WCNT with Communication Constraints -- 3.1.4 Repeatedly Jointly WCNT -- 3.1.5 Numerical Examples -- 3.1.6 Conclusion -- 3.1.7 Appendix -- 3.2 Piecewise Fixed Network Topology: Necessary and Sufficient Conditions -- 3.2.1 Problem Reformulation and Preliminary Results -- 3.2.2 A Subspace Method for Consensus Analysis -- 3.2.3 Extension to Unstable System Dynamics -- 3.2.4 Conclusion.
3.2.5 Appendix: Technical Analysis -- 3.3 Continuously Time-varying Network Topology via Uniform Complete Observability Theory -- 3.3.1 Agent Model and Network Configuration -- 3.3.2 Uniform Complete Observability -- 3.3.3 A Compact Set of Matrix-Valued Functions and Exponential Consensus -- 3.3.4 Further Discussions and Conclusion -- 3.3.5 Appendix: Proof of Lemma 3.56 -- 4 Generic Linear Systems over Directed Switching Network Topology -- 4.1 Discrete-Time Systems with Invertible Input Matrix -- 4.1.1 Agent Model and Network Configuration -- 4.1.2 Theoretical Results and Convergence Analysis -- 4.1.3 Further Analysis and Extensions -- 4.1.4 Numerical Examples -- 4.1.5 Conclusion -- 4.2 Continuous-Time Systems with Invertible Input Matrix -- 4.2.1 Agent Model and Network Configuration -- 4.2.2 Theoretical Results and Convergence Analysis -- 4.2.3 Numerical Examples -- 4.2.4 Conclusion -- 4.3 Non-invertible Input Matrix: an Algebraic and Geometric Perspective -- 4.3.1 System Model and Preliminary Results -- 4.3.2 Convergence Analysis over Any Subinterval Without Connectivity Requirement -- 4.3.3 Synchronization Under Joint Connectivity Condition -- 4.3.4 Numerical Examples -- 4.3.5 Proof of the Main Results -- 4.3.6 Conclusion -- 4.3.7 Appendix -- 5 Extensions to Containment Control -- 5.1 Collective Behavior of Generic Linear Agents … -- 5.1.1 Continuous-Time Setting -- 5.1.2 Discrete-Time Counterpart -- 5.1.3 Application to Consensus and Containment Control -- 5.1.4 Numerical Examples -- 5.1.5 Conclusion -- 5.2 Output Containment Control with Fixed and Switching Topologies -- 5.2.1 Agent Model and Problem Definition -- 5.2.2 A Necessary Condition from Internal Model Principle -- 5.2.3 Output Containment over Fixed Network Topology -- 5.2.4 Output Containment over Dynamic Network -- 5.2.5 Optimal Model-Free Output Containment. 5.2.6 Numerical Examples -- 5.2.7 Conclusion -- 5.3 Containment Control: a Novel State Transition Matrix Perspective -- 5.3.1 Agent Model and Problem Statement -- 5.3.2 The Consensus Pattern in Multi-Leader MASs -- 5.3.3 Containment of Positive Linear Systems -- 5.3.4 Second-Order Agents -- 5.3.5 Conclusion -- References. |
| Record Nr. | UNINA-9910523752603321 |
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Qin Jiahu
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Continuous-time Markov jump linear systems / / Oswaldo L.V. Costa, Marcelo D. Fragoso, Marcos G. Todorov
| Continuous-time Markov jump linear systems / / Oswaldo L.V. Costa, Marcelo D. Fragoso, Marcos G. Todorov |
| Autore | Costa Oswaldo L. V |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (294 p.) |
| Disciplina | 003.76 |
| Altri autori (Persone) |
FragosoMarcelo D
TodorovMarcos G |
| Collana | Probability and its applications |
| Soggetto topico |
Stochastic control theory
Stochastic systems Linear systems Control theory Markov processes |
| ISBN |
1-283-94496-0
3-642-34100-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1.Introduction -- 2.A Few Tools and Notations -- 3.Mean Square Stability -- 4.Quadratic Optimal Control with Complete Observations -- 5.H2 Optimal Control With Complete Observations -- 6.Quadratic and H2 Optimal Control with Partial Observations -- 7.Best Linear Filter with Unknown (x(t), θ(t)) -- 8.H_$infty$ Control -- 9.Design Techniques -- 10.Some Numerical Examples -- A. Coupled Differential and Algebraic Riccati Equations -- B. The Adjoint Operator and Some Auxiliary Results -- References. - Notation and Conventions -- Index. |
| Record Nr. | UNINA-9910437866903321 |
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Costa Oswaldo L. V
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| New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Controllability of singularly perturbed linear time delay systems / / Valery Y. Glizer
| Controllability of singularly perturbed linear time delay systems / / Valery Y. Glizer |
| Autore | Glizer Valery Y. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (429 pages) |
| Disciplina | 003.74 |
| Collana | Systems and Control: Foundations and Applications |
| Soggetto topico |
Linear systems
Control theory Sistemes lineals Teoria de control |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-65951-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 1.1 Real-Life Models -- 1.1.1 Neurosystem Model -- 1.1.2 Sunflower Equation -- 1.1.3 Model of Nuclear Reactor Dynamics -- 1.1.4 Model of Controlled Coupled-Core Nuclear Reactor -- 1.1.5 Car-Following Model: Lane as a Simple Open Curve -- 1.1.6 Car-Following Model: Lane as a Simple Closed Curve -- References -- 2 Singularly Perturbed Linear Time Delay Systems -- 2.1 Introduction -- 2.2 Singularly Perturbed Systems with Small Delays -- 2.2.1 Original System -- 2.2.2 Slow-Fast Decomposition of the Original System -- 2.2.3 Fundamental Matrix Solution -- 2.2.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Small Delays -- 2.2.5 Example 1 -- 2.2.6 Example 2: Tracking Model with Delay -- 2.2.7 Example 3: Analysis of Neurosystem Model -- 2.2.8 Example 4: Analysis of Sunflower Equation -- 2.2.9 Proof of Lemma 2.2 -- 2.2.10 Proof of Theorem 2.1 -- 2.2.10.1 Technical Proposition -- 2.2.10.2 Main Part of the Proof -- 2.3 Singularly Perturbed Systems with Delays of Two Scales -- 2.3.1 Original System -- 2.3.2 Slow-Fast Decomposition of the Original System -- 2.3.3 Fundamental Matrix Solution -- 2.3.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Delays of Two Scales -- 2.3.5 Example 5 -- 2.3.6 Example 6: Dynamics of Nuclear Reactor -- 2.3.7 Example 7: Analysis of Car-Following Model in a Simple Closed Lane -- 2.3.8 Proof of Theorem 2.2 -- 2.4 One Class of Singularly Perturbed Systems with NonsmallDelays -- 2.4.1 Original System -- 2.4.2 Slow-Fast Decomposition of the Original System -- 2.4.3 Fundamental Matrix Solution -- 2.4.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Nonsmall Delays -- 2.4.5 Example 8 -- 2.4.6 Proof of Lemma 2.4 -- 2.4.7 Proof of Theorem 2.4 -- 2.5 Concluding Remarks and Literature Review.
References -- 3 Euclidean Space Output Controllability of Linear Systems with State Delays -- 3.1 Introduction -- 3.2 Systems with Small Delays: Main Notions and Definitions -- 3.2.1 Original System -- 3.2.2 Asymptotic Decomposition of the Original System -- 3.3 Auxiliary Results -- 3.3.1 Output Controllability of a System with State Delays: Necessary and Sufficient Conditions -- 3.3.2 Linear Control Transformation in Systems with Small Delays -- 3.3.2.1 Control Transformation in the Original System -- 3.3.2.2 Asymptotic Decomposition of the Transformed System (3.30)-(3.31), (3.3) -- 3.3.3 Hybrid Set of Riccati-Type Matrix Equations -- 3.3.4 Proof of Lemma 3.1 -- 3.3.4.1 Sufficiency -- 3.3.4.2 Necessity -- 3.3.5 Proof of Lemma 3.5 -- 3.3.6 Proof of Lemma 3.7 -- 3.3.7 Proof of Lemma 3.8 -- 3.3.8 Proof of Lemma 3.9 -- 3.4 Parameter-Free Controllability Conditions for Systems with Small Delays -- 3.4.1 Case of the Standard System (3.1)-(3.2) -- 3.4.2 Case of the Nonstandard System (3.1)-(3.2) -- 3.4.3 Proofs of Theorems 3.1, 3.2, and 3.3 -- 3.4.3.1 Proof of Theorem 3.1 -- 3.4.3.2 Proof of Theorem 3.2 -- 3.4.3.3 Proof of Theorem 3.3 -- 3.5 Special Cases of Controllability for Systems with Small Delays -- 3.5.1 Complete Euclidean Space Controllability -- 3.5.2 Controllability with Respect to x(t) -- 3.5.3 Controllability with Respect to y(t) -- 3.6 Examples: Systems with Small Delays -- 3.6.1 Example 1 -- 3.6.2 Example 2 -- 3.6.3 Example 3 -- 3.6.4 Example 4 -- 3.6.5 Example 5 -- 3.6.6 Example 6: Pursuit-Evasion Engagement with Constant Speeds of Participants -- 3.6.7 Example 7: Pursuit-Evasion Engagement with Variable Speeds of Participants -- 3.6.8 Example 8: Analysis of Controlled Coupled-Core Nuclear Reactor Model -- 3.7 Systems with Delays of Two Scales: Main Notionsand Definitions -- 3.7.1 Original System. 3.7.2 Asymptotic Decomposition of the Original System -- 3.8 Linear Control Transformation in Systems with Delays of Two Scales -- 3.8.1 Control Transformation in the Original System -- 3.8.2 Asymptotic Decomposition of the Transformed System (3.196)-(3.197), (3.187) -- 3.9 Parameter-Free Controllability Conditions for Systems with Delays of Two Scales -- 3.9.1 Case of the Validity of the Assumption (AIII) -- 3.9.2 Case of the Validity of the Assumption (AIV) -- 3.9.3 Special Cases of Controllability -- 3.9.3.1 Complete Euclidean Space Controllability -- 3.9.3.2 Controllability with Respect to x(t) -- 3.9.3.3 Controllability with Respect to y(t) -- 3.9.4 Example 9 -- 3.9.5 Example 10 -- 3.9.6 Example 11: Controlled Car-Following Model in a Simple Open Lane -- 3.10 Concluding Remarks and Literature Review -- References -- 4 Complete Euclidean Space Controllability of Linear Systems with State and Control Delays -- 4.1 Introduction -- 4.2 System with Small State Delays: Main Notions and Definitions -- 4.2.1 Original System -- 4.2.2 Asymptotic Decomposition of the Original System -- 4.3 Preliminary Results -- 4.3.1 Auxiliary System with Small State Delays and Delay-Free Control -- 4.3.2 Output Controllability of the Auxiliary System and Its Slow and Fast Subsystems: Necessary and Sufficient Conditions -- 4.3.2.1 Equivalent Forms of the Auxiliary System -- 4.3.2.2 Output Controllability of the Auxiliary System -- 4.3.2.3 Output Controllability of the Slow and Fast Subsystems Associated with the Auxiliary System -- 4.3.3 Linear Control Transformation in the Original System with Small State Delays -- 4.3.4 Stabilizability of a Parameter-Dependent System with State and Control Delays by a Memory-Less Feedback Control -- 4.3.5 Proof of Lemma 4.8 -- 4.4 Parameter-Free Controllability Conditions for Systems with Small State Delays. 4.4.1 Case of the Standard System (4.1)-(4.2) -- 4.4.2 Case of the Nonstandard System (4.1)-(4.2) -- 4.4.3 Proof of Main Lemma (Lemma 4.9) -- 4.4.3.1 Auxiliary Propositions -- 4.4.3.2 Main Part of the Proof -- 4.4.4 Alternative Approach to Controllability Analysis of the Nonstandard System (4.1)-(4.2) -- 4.4.4.1 Linear Control Transformation in the Auxiliary System (4.40)-(4.42) -- 4.4.4.2 Proof of Lemma 4.10 -- 4.4.4.3 Hybrid Set of Riccati-Type Matrix Equations -- 4.4.4.4 Parameter-Free Controllability Conditions of the Nonstandard System (4.1)-(4.2) -- 4.5 Examples: Systems with Small State and Control Delays -- 4.5.1 Example 1 -- 4.5.2 Example 2 -- 4.5.3 Example 3 -- 4.6 Systems with State Delays of Two Scales: Main Notions and Definitions -- 4.6.1 Original System -- 4.6.2 Asymptotic Decomposition of the Original System -- 4.7 Auxiliary System with State Delays of Two Scales and Delay-Free Control -- 4.7.1 Description of the Auxiliary System and Some of Its Properties -- 4.7.2 Asymptotic Decomposition of the Auxiliary System (4.180)-(4.181) -- 4.7.3 Linear Control Transformation in the Auxiliary System (4.180)-(4.181) -- 4.8 Parameter-Free Controllability Conditions for Systems with Delays of Two Scales -- 4.8.1 Case of the Validity of the Assumption (AV) -- 4.8.2 Case of the Validity of the Assumption (AVI) -- 4.8.3 Example 4 -- 4.8.4 Example 5 -- 4.8.5 Example 6: Analysis of Car-Following Model with State and Control Delays -- 4.9 Concluding Remarks and Literature Review -- References -- 5 First-Order Euclidean Space Controllability Conditions for Linear Systems with Small State Delays -- 5.1 Introduction -- 5.2 Singularly Perturbed System: Main Notions and Definitions -- 5.2.1 Original System -- 5.2.2 Asymptotic Decomposition of the Original System -- 5.3 Auxiliary Results. 5.3.1 Estimates of Solutions to Some Singularly Perturbed Linear Time Delay Matrix Differential Equations -- 5.3.2 Proof of Lemma 5.1 -- 5.3.2.1 Technical Proposition -- 5.3.2.2 Main Part of the Proof -- 5.3.3 Complete Controllability of the Original System and Its Slow Subsystem: Necessary and SufficientConditions -- 5.4 Parameter-Free Controllability Conditions -- 5.4.1 Formulation of Main Assertions -- 5.4.2 Proof of Theorem 5.1 -- 5.4.3 Proof of Lemma 5.2 -- 5.4.4 Proof of Theorem 5.2 -- 5.4.4.1 Euclidean Space Controllability of a Pure Fast System -- 5.4.4.2 Main Part of the Proof -- 5.5 Examples -- 5.5.1 Example 1 -- 5.5.2 Example 2 -- 5.5.3 Example 3 -- 5.5.4 Example 4 -- 5.5.5 Example 5 -- 5.5.6 Example 6 -- 5.5.7 Example 7: Analysis of Controlled Car-Following Model in a Simple Open Lane -- 5.6 Concluding Remarks and Literature Review -- References -- 6 Miscellanies -- 6.1 Introduction -- 6.2 Euclidean Space Controllability of Linear Time Delay Systems with High Gain Control -- 6.2.1 High Gain Control System: Main Notionsand Definitions -- 6.2.1.1 Initial System -- 6.2.1.2 Transformation of the System (6.1) -- 6.2.2 High Dimension Controllability Condition for the System (6.5) -- 6.2.3 Asymptotic Decomposition of the System (6.5) -- 6.2.4 Auxiliary Results -- 6.2.4.1 Linear Control Transformation in the System (6.13)-(6.14) and Some of its Properties -- 6.2.4.2 Asymptotic Decomposition of the Transformed System (6.13), (6.21) -- 6.2.4.3 Block-Wise Estimate of the Solution to the Terminal-Value Problem (6.23) -- 6.2.5 Lower Dimension Parameter-Free Controllability Condition for the System (6.5) -- 6.2.6 Example -- 6.3 Euclidean Space Controllability of Linear Systems with Nonsmall Input Delay -- 6.3.1 Original System -- 6.3.2 Discussion on the Slow-Fast Decomposition of the Original System -- 6.3.3 Auxiliary Results. 6.3.3.1 Necessary and Sufficient Controllability Conditions of the Original System. |
| Record Nr. | UNISA-996466544903316 |
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Glizer Valery Y.
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| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Controllability of singularly perturbed linear time delay systems / / Valery Y. Glizer
| Controllability of singularly perturbed linear time delay systems / / Valery Y. Glizer |
| Autore | Glizer Valery Y. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (429 pages) |
| Disciplina | 003.74 |
| Collana | Systems and Control: Foundations and Applications |
| Soggetto topico |
Linear systems
Control theory Sistemes lineals Teoria de control |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-65951-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 1.1 Real-Life Models -- 1.1.1 Neurosystem Model -- 1.1.2 Sunflower Equation -- 1.1.3 Model of Nuclear Reactor Dynamics -- 1.1.4 Model of Controlled Coupled-Core Nuclear Reactor -- 1.1.5 Car-Following Model: Lane as a Simple Open Curve -- 1.1.6 Car-Following Model: Lane as a Simple Closed Curve -- References -- 2 Singularly Perturbed Linear Time Delay Systems -- 2.1 Introduction -- 2.2 Singularly Perturbed Systems with Small Delays -- 2.2.1 Original System -- 2.2.2 Slow-Fast Decomposition of the Original System -- 2.2.3 Fundamental Matrix Solution -- 2.2.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Small Delays -- 2.2.5 Example 1 -- 2.2.6 Example 2: Tracking Model with Delay -- 2.2.7 Example 3: Analysis of Neurosystem Model -- 2.2.8 Example 4: Analysis of Sunflower Equation -- 2.2.9 Proof of Lemma 2.2 -- 2.2.10 Proof of Theorem 2.1 -- 2.2.10.1 Technical Proposition -- 2.2.10.2 Main Part of the Proof -- 2.3 Singularly Perturbed Systems with Delays of Two Scales -- 2.3.1 Original System -- 2.3.2 Slow-Fast Decomposition of the Original System -- 2.3.3 Fundamental Matrix Solution -- 2.3.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Delays of Two Scales -- 2.3.5 Example 5 -- 2.3.6 Example 6: Dynamics of Nuclear Reactor -- 2.3.7 Example 7: Analysis of Car-Following Model in a Simple Closed Lane -- 2.3.8 Proof of Theorem 2.2 -- 2.4 One Class of Singularly Perturbed Systems with NonsmallDelays -- 2.4.1 Original System -- 2.4.2 Slow-Fast Decomposition of the Original System -- 2.4.3 Fundamental Matrix Solution -- 2.4.4 Estimates of Solutions to Singularly Perturbed Matrix Differential Systems with Nonsmall Delays -- 2.4.5 Example 8 -- 2.4.6 Proof of Lemma 2.4 -- 2.4.7 Proof of Theorem 2.4 -- 2.5 Concluding Remarks and Literature Review.
References -- 3 Euclidean Space Output Controllability of Linear Systems with State Delays -- 3.1 Introduction -- 3.2 Systems with Small Delays: Main Notions and Definitions -- 3.2.1 Original System -- 3.2.2 Asymptotic Decomposition of the Original System -- 3.3 Auxiliary Results -- 3.3.1 Output Controllability of a System with State Delays: Necessary and Sufficient Conditions -- 3.3.2 Linear Control Transformation in Systems with Small Delays -- 3.3.2.1 Control Transformation in the Original System -- 3.3.2.2 Asymptotic Decomposition of the Transformed System (3.30)-(3.31), (3.3) -- 3.3.3 Hybrid Set of Riccati-Type Matrix Equations -- 3.3.4 Proof of Lemma 3.1 -- 3.3.4.1 Sufficiency -- 3.3.4.2 Necessity -- 3.3.5 Proof of Lemma 3.5 -- 3.3.6 Proof of Lemma 3.7 -- 3.3.7 Proof of Lemma 3.8 -- 3.3.8 Proof of Lemma 3.9 -- 3.4 Parameter-Free Controllability Conditions for Systems with Small Delays -- 3.4.1 Case of the Standard System (3.1)-(3.2) -- 3.4.2 Case of the Nonstandard System (3.1)-(3.2) -- 3.4.3 Proofs of Theorems 3.1, 3.2, and 3.3 -- 3.4.3.1 Proof of Theorem 3.1 -- 3.4.3.2 Proof of Theorem 3.2 -- 3.4.3.3 Proof of Theorem 3.3 -- 3.5 Special Cases of Controllability for Systems with Small Delays -- 3.5.1 Complete Euclidean Space Controllability -- 3.5.2 Controllability with Respect to x(t) -- 3.5.3 Controllability with Respect to y(t) -- 3.6 Examples: Systems with Small Delays -- 3.6.1 Example 1 -- 3.6.2 Example 2 -- 3.6.3 Example 3 -- 3.6.4 Example 4 -- 3.6.5 Example 5 -- 3.6.6 Example 6: Pursuit-Evasion Engagement with Constant Speeds of Participants -- 3.6.7 Example 7: Pursuit-Evasion Engagement with Variable Speeds of Participants -- 3.6.8 Example 8: Analysis of Controlled Coupled-Core Nuclear Reactor Model -- 3.7 Systems with Delays of Two Scales: Main Notionsand Definitions -- 3.7.1 Original System. 3.7.2 Asymptotic Decomposition of the Original System -- 3.8 Linear Control Transformation in Systems with Delays of Two Scales -- 3.8.1 Control Transformation in the Original System -- 3.8.2 Asymptotic Decomposition of the Transformed System (3.196)-(3.197), (3.187) -- 3.9 Parameter-Free Controllability Conditions for Systems with Delays of Two Scales -- 3.9.1 Case of the Validity of the Assumption (AIII) -- 3.9.2 Case of the Validity of the Assumption (AIV) -- 3.9.3 Special Cases of Controllability -- 3.9.3.1 Complete Euclidean Space Controllability -- 3.9.3.2 Controllability with Respect to x(t) -- 3.9.3.3 Controllability with Respect to y(t) -- 3.9.4 Example 9 -- 3.9.5 Example 10 -- 3.9.6 Example 11: Controlled Car-Following Model in a Simple Open Lane -- 3.10 Concluding Remarks and Literature Review -- References -- 4 Complete Euclidean Space Controllability of Linear Systems with State and Control Delays -- 4.1 Introduction -- 4.2 System with Small State Delays: Main Notions and Definitions -- 4.2.1 Original System -- 4.2.2 Asymptotic Decomposition of the Original System -- 4.3 Preliminary Results -- 4.3.1 Auxiliary System with Small State Delays and Delay-Free Control -- 4.3.2 Output Controllability of the Auxiliary System and Its Slow and Fast Subsystems: Necessary and Sufficient Conditions -- 4.3.2.1 Equivalent Forms of the Auxiliary System -- 4.3.2.2 Output Controllability of the Auxiliary System -- 4.3.2.3 Output Controllability of the Slow and Fast Subsystems Associated with the Auxiliary System -- 4.3.3 Linear Control Transformation in the Original System with Small State Delays -- 4.3.4 Stabilizability of a Parameter-Dependent System with State and Control Delays by a Memory-Less Feedback Control -- 4.3.5 Proof of Lemma 4.8 -- 4.4 Parameter-Free Controllability Conditions for Systems with Small State Delays. 4.4.1 Case of the Standard System (4.1)-(4.2) -- 4.4.2 Case of the Nonstandard System (4.1)-(4.2) -- 4.4.3 Proof of Main Lemma (Lemma 4.9) -- 4.4.3.1 Auxiliary Propositions -- 4.4.3.2 Main Part of the Proof -- 4.4.4 Alternative Approach to Controllability Analysis of the Nonstandard System (4.1)-(4.2) -- 4.4.4.1 Linear Control Transformation in the Auxiliary System (4.40)-(4.42) -- 4.4.4.2 Proof of Lemma 4.10 -- 4.4.4.3 Hybrid Set of Riccati-Type Matrix Equations -- 4.4.4.4 Parameter-Free Controllability Conditions of the Nonstandard System (4.1)-(4.2) -- 4.5 Examples: Systems with Small State and Control Delays -- 4.5.1 Example 1 -- 4.5.2 Example 2 -- 4.5.3 Example 3 -- 4.6 Systems with State Delays of Two Scales: Main Notions and Definitions -- 4.6.1 Original System -- 4.6.2 Asymptotic Decomposition of the Original System -- 4.7 Auxiliary System with State Delays of Two Scales and Delay-Free Control -- 4.7.1 Description of the Auxiliary System and Some of Its Properties -- 4.7.2 Asymptotic Decomposition of the Auxiliary System (4.180)-(4.181) -- 4.7.3 Linear Control Transformation in the Auxiliary System (4.180)-(4.181) -- 4.8 Parameter-Free Controllability Conditions for Systems with Delays of Two Scales -- 4.8.1 Case of the Validity of the Assumption (AV) -- 4.8.2 Case of the Validity of the Assumption (AVI) -- 4.8.3 Example 4 -- 4.8.4 Example 5 -- 4.8.5 Example 6: Analysis of Car-Following Model with State and Control Delays -- 4.9 Concluding Remarks and Literature Review -- References -- 5 First-Order Euclidean Space Controllability Conditions for Linear Systems with Small State Delays -- 5.1 Introduction -- 5.2 Singularly Perturbed System: Main Notions and Definitions -- 5.2.1 Original System -- 5.2.2 Asymptotic Decomposition of the Original System -- 5.3 Auxiliary Results. 5.3.1 Estimates of Solutions to Some Singularly Perturbed Linear Time Delay Matrix Differential Equations -- 5.3.2 Proof of Lemma 5.1 -- 5.3.2.1 Technical Proposition -- 5.3.2.2 Main Part of the Proof -- 5.3.3 Complete Controllability of the Original System and Its Slow Subsystem: Necessary and SufficientConditions -- 5.4 Parameter-Free Controllability Conditions -- 5.4.1 Formulation of Main Assertions -- 5.4.2 Proof of Theorem 5.1 -- 5.4.3 Proof of Lemma 5.2 -- 5.4.4 Proof of Theorem 5.2 -- 5.4.4.1 Euclidean Space Controllability of a Pure Fast System -- 5.4.4.2 Main Part of the Proof -- 5.5 Examples -- 5.5.1 Example 1 -- 5.5.2 Example 2 -- 5.5.3 Example 3 -- 5.5.4 Example 4 -- 5.5.5 Example 5 -- 5.5.6 Example 6 -- 5.5.7 Example 7: Analysis of Controlled Car-Following Model in a Simple Open Lane -- 5.6 Concluding Remarks and Literature Review -- References -- 6 Miscellanies -- 6.1 Introduction -- 6.2 Euclidean Space Controllability of Linear Time Delay Systems with High Gain Control -- 6.2.1 High Gain Control System: Main Notionsand Definitions -- 6.2.1.1 Initial System -- 6.2.1.2 Transformation of the System (6.1) -- 6.2.2 High Dimension Controllability Condition for the System (6.5) -- 6.2.3 Asymptotic Decomposition of the System (6.5) -- 6.2.4 Auxiliary Results -- 6.2.4.1 Linear Control Transformation in the System (6.13)-(6.14) and Some of its Properties -- 6.2.4.2 Asymptotic Decomposition of the Transformed System (6.13), (6.21) -- 6.2.4.3 Block-Wise Estimate of the Solution to the Terminal-Value Problem (6.23) -- 6.2.5 Lower Dimension Parameter-Free Controllability Condition for the System (6.5) -- 6.2.6 Example -- 6.3 Euclidean Space Controllability of Linear Systems with Nonsmall Input Delay -- 6.3.1 Original System -- 6.3.2 Discussion on the Slow-Fast Decomposition of the Original System -- 6.3.3 Auxiliary Results. 6.3.3.1 Necessary and Sufficient Controllability Conditions of the Original System. |
| Record Nr. | UNINA-9910483576203321 |
|
Glizer Valery Y.
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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Linear systems
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