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Algorithms for Sparse Linear Systems / / Jennifer Scott, Miroslav Tůma
| Algorithms for Sparse Linear Systems / / Jennifer Scott, Miroslav Tůma |
| Autore | Scott Jennifer |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing, , 2023 |
| Descrizione fisica | 1 online resource (xix, 242 pages) : illustrations (some color) |
| Disciplina | 511.8 |
| Collana | Nečas Center Series |
| Soggetto topico |
Algorithms
Matrius disperses Sistemes lineals Algorismes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-25820-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | An introduction to sparse matrices Sparse matrices and their graphs Introduction to matrix factorizations Sparse Cholesky sovler: The symbolic phase Sparse Cholesky solver: The factorization phase Sparse LU factorizations Stability, ill-conditioning and symmetric indefinite factorizations Sparse matrix ordering algorithms Algebraic preconditioning and approximate factorizations Incomplete factorizations Sparse approximate inverse preconditioners. |
| Record Nr. | UNINA-9910717411903321 |
Scott Jennifer
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| Cham : , : Springer International Publishing, , 2023 | ||
| 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 |
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Glizer Valery Y.
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| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Descriptor systems of integer and fractional orders / / Tadeusz Kaczorek, Kamil Borawski
| Descriptor systems of integer and fractional orders / / Tadeusz Kaczorek, Kamil Borawski |
| Autore | Kaczorek T (Tadeusz), <1932-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (xiv, 252 pages) : illustrations |
| Disciplina | 003.83 |
| Collana | Studies in systems, decision and control |
| Soggetto topico |
Discrete-time systems
Linear time invariant systems Sistemes de temps discret Sistemes lineals |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-72480-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Descriptor Linear Systems Fractional Descriptor Linear Systems Stability of Positive Descriptor Systems Appendix |
| Record Nr. | UNINA-9910483065503321 |
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Kaczorek T (Tadeusz), <1932->
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Krylov Subspace Methods for Linear Systems : Principles of Algorithms / / by Tomohiro Sogabe
| Krylov Subspace Methods for Linear Systems : Principles of Algorithms / / by Tomohiro Sogabe |
| Autore | Sogabe Tomohiro |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (233 pages) |
| Disciplina | 518.1 |
| Collana | Springer Series in Computational Mathematics |
| Soggetto topico |
Numerical analysis
Mathematical models Algorithms Numerical Analysis Mathematical Modeling and Industrial Mathematics Sistemes lineals Anàlisi numèrica Algorismes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811985324
9789811985317 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction to Numerical Methods for Solving Linear Systems -- Some Applications to Computational Science and Data Science -- Classification and Theory of Krylov Subspace Methods -- Applications to Shifted Linear Systems -- Applications to Matrix Functions. |
| Record Nr. | UNINA-9910645887403321 |
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Sogabe Tomohiro
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Linear systems / / Gordon Blower
| Linear systems / / Gordon Blower |
| Autore | Blower G (Gordon) |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2023] |
| Descrizione fisica | 1 online resource (417 pages) |
| Disciplina | 629.8 |
| Collana | Mathematical Engineering |
| Soggetto topico |
Automatic control
Automatic control - Data processing Sistemes lineals |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031212406
9783031212390 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Linear Systems and Their Description -- 1.1 Linear Systems and Their Description -- 1.2 Feedback -- 1.3 Linear Differential Equations -- 1.4 Damped Harmonic Oscillator -- 1.5 Reduction of Order of Linear ODE -- 1.6 Exercises -- 2 Solving Linear Systems by Matrix Theory -- 2.1 Matrix Terminology -- 2.2 Characteristic Polynomial -- 2.3 Norm of a Vector -- 2.4 Cauchy-Schwarz Inequality -- 2.5 Matrix Exponential exp(A) or expm (A) -- 2.6 Exponential of a Diagonable Matrix -- 2.7 Solving MIMO (A,B,C,D) -- 2.8 Rational Functions -- 2.9 Block Matrices -- 2.10 The Transfer Function of (A,B,C,D) -- 2.11 Realization with a SISO -- 2.12 Exercises -- 3 Eigenvalues and Block Decompositions of Matrices -- 3.1 The Transfer Function of Similar SISOs (A,B,C,D) -- 3.2 Jordan Blocks -- 3.3 Exponentials and Eigenvalues of Complex Matrices -- 3.4 Exponentials and the Resolvent -- 3.5 Schur Complements -- 3.6 Self-adjoint Matrices -- 3.7 Positive Definite Matrices -- 3.8 Linear Fractional Transformations -- 3.9 Stable Matrices -- 3.10 Dissipative Matrices -- 3.11 A Determinant Formula -- 3.12 Observability and Controllability -- 3.13 Kalman's Decomposition -- 3.14 Kronecker Product of Matrices -- 3.15 Exercises -- 4 Laplace Transforms -- 4.1 Laplace Transforms -- 4.2 Laplace Convolution -- 4.3 Laplace Uniqueness Theorem -- 4.4 Laplace Transform of a Differential Equation -- 4.5 Solving MIMO by Laplace Transforms -- 4.6 Partial Fractions -- 4.7 Dirichlet's Integral and Heaviside's Expansions -- 4.8 Final Value Theorem -- 4.9 Laplace Transforms of Periodic Functions -- 4.10 Fourier Cosine Transform -- 4.11 Impulse Response -- 4.12 Transmitting Signals -- 4.13 Exercises -- 5 Transfer Functions, Frequency Response, Realization and Stability -- 5.1 Winding Numbers -- 5.2 Realization -- 5.3 Frequency Response -- 5.4 Nyquist's Locus.
5.5 Gain and Phase -- 5.6 BIBO Stability -- 5.7 Undamped Harmonic Oscillator: Marginal Stability and Resonance -- 5.8 BIBO Stability in Terms of Eigenvalues of A -- 5.9 Maxwell's Stability Problem -- 5.10 Stable Rational Transfer Functions -- 5.11 Nyquist's Criterion for Stability of T -- 5.12 Nyquist's Criterion Proof -- 5.13 M and N Circles -- 5.14 Exercises -- 6 Algebraic Characterizations of Stability -- 6.1 Feedback Control -- 6.2 PID Controllers -- 6.3 Stable Cubics -- 6.4 Hurwitz's Stability Criterion -- 6.5 Units and Factors -- 6.6 Euclidean Algorithm and Principal Ideal Domains -- 6.7 Ideals in the Complex Polynomials -- 6.8 Highest Common Factor and Common Zeros -- 6.9 Rings of Fractions -- 6.10 Coprime Factorization in the Stable Rational Functions -- 6.11 Controlling Rational Systems -- 6.12 Invariant Factors -- 6.13 Matrix Factorizations to Stabilize MIMO -- 6.14 Inverse Laplace Transforms of Strictly Proper Rational Functions -- 6.15 Differential Rings -- 6.16 Bessel Functions of Integral Order -- 6.17 Exercises -- 7 Stability and Transfer Functions via Linear Algebra -- 7.1 Lyapunov's Criterion -- 7.2 Sylvester's Equation AY+YB+C=0 -- 7.3 A Solution of Lyapunov's Equation AL+LA' +P=0 -- 7.4 Stable and Dissipative Linear Systems -- 7.5 Almost Stable Linear Systems -- 7.6 Simultaneous Diagonalization -- 7.7 A Linear Matrix Inequality -- 7.8 Differential Equations Relating to Sylvester's Equation -- 7.9 Transfer Functions tf -- 7.10 Small Groups of Matrices -- 7.11 How to Convert Complex Matrices into Real Matrices -- 7.12 Periods -- 7.13 Discrete Fourier Transform -- 7.14 Exercises -- 8 Discrete Time Systems -- 8.1 Discrete-Time Linear Systems -- 8.2 Transfer Function for a Discrete Time Linear System -- 8.3 Correspondence Between Continuous- and Discrete-Time Systems -- 8.4 Chebyshev Polynomials and Filters. 8.5 Hankel Matrices and Moments -- 8.6 Orthogonal Polynomials -- 8.7 Hankel Determinants -- 8.8 Laguerre Polynomials -- 8.9 Three-Term Recurrence Relation -- 8.10 Moments via Discrete Time Linear Systems -- 8.11 Floquet Multipliers -- 8.12 Exercises -- 9 Random Linear Systems and Green's Functions -- 9.1 ARMA Process -- 9.2 Distributions on a Bounded Interval -- 9.3 Cauchy Transforms -- 9.4 Herglotz Functions -- 9.5 Green's Functions -- 9.6 Random Diagonal Transformations -- 9.7 Wigner Matrices -- 9.8 Pastur's Theorem -- 9.9 May-Wigner Model -- 9.10 Semicircle Addition Law -- 9.11 Matrix Version of Pastur's Fixed Point Equation -- 9.12 Rank One Perturbations on Green's Functions -- 9.13 Exercises -- 10 Hilbert Spaces -- 10.1 Hilbert Sequence Space -- 10.2 Hardy Space on the Disc -- 10.3 Subspaces and Blocks -- 10.4 Shifts and Multiplication Operators -- 10.5 Canonical Model -- 10.6 Hardy Space on the Right Half-Plane -- 10.7 Paley-Wiener Theorem -- 10.8 Rational Filters -- 10.9 Shifts on L2 -- 10.10 The Telegraph Equation as a Linear System -- 10.11 Exercises -- 11 Wireless Transmission and Wavelets -- 11.1 Frequency Band Limited Functions and Sampling -- 11.2 The Shannon Wavelet -- 11.3 Telatar's Model of Wireless Communication -- 11.4 Exercises -- 12 Solutions to Selected Exercises -- Glossary of Linear Systems Terminology -- A MATLAB Commands for Matrices -- B SciLab Matrix Operations -- References -- Index. |
| Record Nr. | UNISA-996508571903316 |
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Blower G (Gordon)
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| Cham, Switzerland : , : Springer International Publishing, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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- Algorismes (2)
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