LEADER 05581nam 2200565Ia 450 001 9910437873603321 005 20200520144314.0 010 $a3-642-34928-5 024 7 $a10.1007/978-3-642-34928-7 035 $a(OCoLC)834089848 035 $a(MiFhGG)GVRL6VYW 035 $a(CKB)2550000001045657 035 $a(MiAaPQ)EBC1206068 035 $a(EXLCZ)992550000001045657 100 $a20130312d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 00$aSurveys in differential-algebraic equations I /$f[edited by] Achim Ilchmann, Timo Reis 205 $a1st ed. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (vii, 231 pages) $cillustrations 225 0 $aDifferential-algebraic equations forum 300 $aDescription based upon print version of record. 311 $a3-642-34927-7 320 $aIncludes bibliographical references and index. 327 $aSurveys in Differential-Algebraic Equations I; Preface; Contents; Controllability of Linear Differential-Algebraic Systems-A Survey; 1 Introduction; 2 Controllability Concepts, p. 5; 3 Solutions, Relations and Normal Forms, p. 15; 4 Algebraic Criteria, p. 30; 5 Feedback, Stability and Autonomous System p. 36; 6 Invariant Subspaces, p. 46; 7 Kalman Decomposition, p. 50; 2 Controllability Concepts; 3 Solutions, Relations and Normal Forms; 3.1 System and Feedback Equivalence; 3.2 A Normal Form Under System Equivalence; 3.3 A Normal Form under Feedback Equivalence; 4 Criteria of Hautus Type 327 $a5 Feedback, Stability and Autonomous Systems5.1 Stabilizability, Autonomy and Stability; 5.2 Stabilization by Feedback; 5.3 Control in the Behavioral Sense; 6 Invariant Subspaces; 7 Kalman Decomposition; References; Robust Stability of Differential-Algebraic Equations; 1 Introduction; 2 Robust Stability of Linear Time-Invariant DAEs; 2.1 Stability Radii for Linear Time-Invariant DAEs; 2.2 Dependence of Stability Radii on the Data; 3 Robust Stability of Linear Time-Varying DAEs; 3.1 Stability Radii for Linear Time-Varying DAEs; 3.2 Dependence of Stability Radii on the Data; 4 Discussion 327 $aReferencesDAEs in Circuit Modelling: A Survey; 1 Introduction; 2 Model Families for Classical Circuits; 2.1 Graph-Theoretic Results; 2.2 Some Preliminaries from Circuit Theory; Kirchhoff Laws; Component Relations; Topologically Degenerate Configurations; Example; 2.3 Nodal Analysis. MNA; 2.4 Branch-Oriented Models, Tree-Based Formulations and Hybrid Analysis; Tree-Based Models; Hybrid Analysis; 2.5 Multiport Model and Hessenberg Form; 2.6 Loop Analysis; 2.7 DAE Form of the Models; 3 The Index of DAE Circuit Models; 3.1 On the Index Notion; The Tractability Index; Other Index Notions 327 $aSolvability3.2 Nodal Models; 3.2.1 Passive Problems; 3.2.2 Low Index Configurations in the Non-passive Context; 3.3 Branch-Oriented and Hybrid Models; 3.3.1 Branch-Oriented Models; 3.3.2 Hybrid Models of Passive Circuits; 3.3.3 Hybrid Models of Non-passive Circuits; 3.4 Example; MNA; Hybrid Analysis; 4 Memristors and Mem-Devices; 4.1 Memristors; 4.2 Memcapacitors, Meminductors and Higher Order Devices; 4.3 DAE Models of Circuits with Mem-Devices; 5 Dynamical Aspects; 5.1 The State Formulation Problem; 5.2 Singularities and Impasse Phenomena; 5.3 Qualitative Properties in the Semistate Context 327 $a6 Other Topics in DAE-Based Circuit ModellingModel Reduction; Coupled Problems; Numerics in Circuit Simulation via DAE Models; Other Topics; 7 Concluding Remarks; References; Solution Concepts for Linear DAEs: A Survey; 1 Introduction; 2 Classical Solutions; 2.1 The Kronecker and Weierstraß Canonical Forms; 2.2 Solution Formulas Based on the Wong Sequences: General Case; 2.3 Existence and Uniqueness of Solutions with Respect to In- and Outputs; 2.4 Solution Formulas Based on the Wong Sequences: Regular Case; 2.5 The Drazin Inverse Solution Formula; 2.6 Time-Varying DAEs 327 $a3 Inconsistent Initial Values and Distributional Solutions 330 $aThe need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to the strong relation to (ordinary) differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in -  Controllability for linear DAEs -  Port-Hamiltonian differential-algebraic systems -  Robustness of DAEs -  Solution concepts for DAEs -  DAEs in circuit modeling. The results in the individual chapters are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study. 410 0$aDifferential-algebraic equations forum. 606 $aDifferential equations 606 $aDifferential-algebraic equations 615 0$aDifferential equations. 615 0$aDifferential-algebraic equations. 676 $a512.56 701 $aIlchmann$b Achim$0768197 701 $aReis$b Timo$0768198 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437873603321 996 $aSurveys in differential-algebraic equations I$94200567 997 $aUNINA