Surveys in Differential-algebraic Equations I

Cover......Page 1
Surveys in Differential-Algebraic Equations I......Page 4
Preface......Page 6
Contents......Page 8
Controllability of Linear Differential-Algebraic Systems-A Survey......Page 9
1 Introduction......Page 10
3 Solutions, Relations and Normal Forms, p. 15......Page 11
7 Kalman Decomposition, p. 50......Page 12
2 Controllability Concepts......Page 13
3.1 System and Feedback Equivalence......Page 23
3.2 A Normal Form Under System Equivalence......Page 27
3.3 A Normal Form under Feedback Equivalence......Page 31
4 Criteria of Hautus Type......Page 38
5.1 Stabilizability, Autonomy and Stability......Page 44
5.2 Stabilization by Feedback......Page 47
5.3 Control in the Behavioral Sense......Page 51
6 Invariant Subspaces......Page 54
7 Kalman Decomposition......Page 58
References......Page 63
1 Introduction......Page 70
2 Robust Stability of Linear Time-Invariant DAEs......Page 74
2.1 Stability Radii for Linear Time-Invariant DAEs......Page 75
2.2 Dependence of Stability Radii on the Data......Page 84
3 Robust Stability of Linear Time-Varying DAEs......Page 85
3.1 Stability Radii for Linear Time-Varying DAEs......Page 89
3.2 Dependence of Stability Radii on the Data......Page 93
References......Page 98
1 Introduction......Page 103
2 Model Families for Classical Circuits......Page 105
2.1 Graph-Theoretic Results......Page 106
Component Relations......Page 108
Example......Page 109
2.3 Nodal Analysis. MNA......Page 111
Tree-Based Models......Page 113
Hybrid Analysis......Page 114
2.5 Multiport Model and Hessenberg Form......Page 115
2.7 DAE Form of the Models......Page 116
3 The Index of DAE Circuit Models......Page 117
The Tractability Index......Page 118
Other Index Notions......Page 119
3.2.1 Passive Problems......Page 120
3.2.2 Low Index Configurations in the Non-passive Context......Page 122
3.3.2 Hybrid Models of Passive Circuits......Page 123
3.3.3 Hybrid Models of Non-passive Circuits......Page 124
MNA......Page 125
Hybrid Analysis......Page 126
4.1 Memristors......Page 127
4.2 Memcapacitors, Meminductors and Higher Order Devices......Page 128
4.3 DAE Models of Circuits with Mem-Devices......Page 129
5.1 The State Formulation Problem......Page 130
5.2 Singularities and Impasse Phenomena......Page 131
5.3 Qualitative Properties in the Semistate Context......Page 132
Other Topics......Page 133
References......Page 134
1 Introduction......Page 143
2.1 The Kronecker and Weierstraß Canonical Forms......Page 145
2.2 Solution Formulas Based on the Wong Sequences: General Case......Page 149
2.3 Existence and Uniqueness of Solutions with Respect to In- and Outputs......Page 151
2.4 Solution Formulas Based on the Wong Sequences: Regular Case......Page 153
2.5 The Drazin Inverse Solution Formula......Page 155
2.6 Time-Varying DAEs......Page 157
3 Inconsistent Initial Values and Distributional Solutions......Page 158
4 Laplace Transform Approaches......Page 161
5 Distributional Solutions......Page 167
5.1 The Problem of Distributional Restrictions......Page 168
5.2 Cobb's Space of Piecewise-Continuous Distributions......Page 169
5.3 Impulsive-Smooth Distributions as Solution Space......Page 171
5.4 Piecewise-Smooth Distributions as Solution Space......Page 174
References......Page 176
1 Introduction to Port-Hamiltonian Differential-Algebraic Systems......Page 179
1.1 A Motivating Example......Page 180
2 Definition of Port-Hamiltonian Systems......Page 183
2.1 Dirac Structures......Page 184
2.2 Energy Storage......Page 186
2.3 Energy Dissipation......Page 187
2.4 External Ports......Page 188
2.5 Resulting Port-Hamiltonian Dynamics......Page 189
2.6 Port-Hamiltonian Systems and Passivity......Page 191
2.7 Modulated Dirac Structures and Port-Hamiltonian Systems on Manifolds......Page 192
2.7.1 Kinematic Constraints in Mechanics......Page 193
2.8 Input-State-Output Port-Hamiltonian Systems......Page 195
3 Representations of Dirac Structures and Port-Hamiltonian Systems......Page 197
3.1.1 Kernel and Image Representation......Page 198
3.1.3 Hybrid Input-Output Representation......Page 200
3.2 Representations of Port-Hamiltonian Systems......Page 201
4.1 Analysis and Elimination of Algebraic Constraints......Page 206
4.1.1 The Linear Index One Case......Page 208
4.1.2 Elimination of Kinematic Constraints......Page 209
4.2 The Geometric Description of Algebraic Constraints of Port-Hamiltonian DAEs......Page 212
4.2.1 Algebraic Constraints in the Canonical Coordinate Representation......Page 213
4.3 Casimirs of Port-Hamiltonian DAEs......Page 214
4.4 Stability Analysis of Port-Hamiltonian DAEs......Page 215
4.5 Ill-posedness Due to Nonlinear Resistive Characteristics......Page 217
5 Port-Hamiltonian Systems with Variable Topology......Page 219
6 Interconnection of Port-Hamiltonian Systems and Composition of Dirac Structures......Page 221
6.1 Composition of Dirac Structures......Page 222
7 Integrability of Modulated Dirac Structures......Page 225
References......Page 230
Index......Page 233