Differential algebraic systems: analytical aspects and circuit applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ [u.a.]
World Scientific
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 330 S. |
| ISBN: | 9812791809 9789812791801 |
Internformat
MARC
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| 100 | 1 | |a Riaza, Ricardo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential algebraic systems |b analytical aspects and circuit applications |c Ricardo Riaza |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XIV, 330 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Differential-algebraic equations | |
| 650 | 4 | |a Electric circuits |x Mathematical models | |
| 650 | 0 | 7 | |a Differential-algebraisches Gleichungssystem |0 (DE-588)4229517-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137742436663296 |
|---|---|
| adam_text | Contents
Preface vii
1. Introduction 1
1.1 Historical remarks: Different origins, different names ... 2
1.2 DAE analysis......................... 4
1.2.1 Indices........................ 5
1.2.2 Dynamics and singularities............. 8
1.2.3 Numerical aspects.................. 10
1.3 State vs. semistate modeling ................ 11
1.4 Formulations......................... 12
1.4.1 Input-output descriptions.............. 13
1.4.2 Leading terms.................... 15
1.4.3 Semiexplicit, semilinear and quasilinear DAEs . . 16
1.5 Contents and structure of the book............. 20
Analytical aspects of DAEs 23
2. Linear DAEs and projector-based methods 25
2.1 Linear time-invariant DAEs................. 26
2.1.1 Matrix pencils and the Kronecker canonical form 27
2.1.2 Solving linear time-invariant DAEs via the KCF . 28
2.1.3 A glance at projector-based techniques...... 29
2.2 Properly stated linear time-varying DAEs......... 35
2.2.1 On standard form index one problems....... 36
2.2.2 Properly stated leading terms........... 38
2.2.3 P-projectors: Matrix chain and the tractability index 39
2.2.4 The II-framework.................. 43
2.2.5 Decoupling...................... 51
2.2.6 A tutorial example ................. 65
2.2.7 Regular points.................... 74
xii Contents
2.3 Standard form linear DAEs................. 75
2.3.1 The tractability index of standard form DAEs . . 75
2.3.2 Decoupling...................... 78
2.3.3 Time-invariant problems revisited......... 79
2.4 Other approaches for linear DAEs: Reduction techniques 81
3. Nonlinear DAEs and reduction methods 83
3.1 Semiexplicit index one DAEs................ 85
3.2 Hessenberg systems...................... 88
3.3 Some notions from differential geometry.......... 90
3.4 Quasilinear DAEs: The geometric index.......... 93
3.4.1 The framework of Rabier and Rheinboldt..... 94
3.4.2 Index zero and index one points.......... 97
3.4.3 Higher index points................. 103
3.4.4 Manifold sequences and locally regular DAEs . . . 108
3.4.5 Local equivalence.................. Ill
3.4.6 Examples....................... 118
3.4.7 Nonautonomous problems ............. 123
3.5 Dynamical aspects...................... 130
3.6 Reduction methods for fully nonlinear DAEs ....... 133
3.7 The differentiation index and derivative arrays...... 134
4. Singularities 137
4.1 What is a singular DAE? .................. 137
4.2 Singularities of properly stated linear time-varying DAEs 139
4.2.1 Classification of singular points .......... 140
4.2.2 Decoupling...................... 145
4.3 Singularities of standard form linear time-varying DAEs . 154
4.3.1 Classification..................... 154
4.3.2 Decoupling...................... 156
4.3.3 Analytic problems.................. 157
4.4 Singularities of autonomous quasilinear DAEs....... 160
4.4.1 Quasilinear ODEs and impasse phenomena .... 162
4.4.2 Singular points of quasilinear DAEs........ 168
4.4.3 A reduction framework for singular problems ... 171
4.4.4 Dynamical aspects.................. 179
4.4.5 Singular semiexplicit index one DAEs....... 181
4.4.6 Examples....................... 184
Contents xiii
Semistate models of electrical circuits 191
5. Nodal analysis 193
5.1 Background on graphs and electrical circuits........ 195
5.1.1 Graphs and digraphs................ 196
5.1.2 Elementary aspects of circuit theory........ 203
5.2 Formulation of nodal models ................ 212
5.2.1 Node Tableau Analysis............... 213
5.2.2 Augmented Nodal Analysis............. 214
5.2.3 Modified Nodal Analysis.............. 215
5.3 Index analysis: Fundamentals................ 216
5.3.1 Structural form of nodal models.......... 216
5.3.2 On the tractability index of quasilinear DAEs . . 218
5.4 Index analysis: Passive circuits............... 219
5.4.1 Tableau equations and Augmented Nodal Analysis 220
5.4.2 Modified Nodal Analysis.............. 232
5.5 Index analysis: Tree methods for non-passive circuits . . . 236
5.5.1 Augmented Nodal Analysis ............. 237
5.5.2 Modified Nodal Analysis.............. 243
6. Branch-oriented methods 255
6.1 Branch-oriented semistate models.............. 257
6.1.1 The basic model................... 258
6.1.2 Tree-based formulations............... 259
6.1.3 The state formulation problem........... 262
6.2 Geometric index analysis and reduction of branch models 264
6.2.1 Operating points................... 265
6.2.2 Implicitly described resistors and strict passivity . 265
6.2.3 Multiport reduction................. 271
6.2.4 Index characterization................ 279
6.2.5 State space reduction................ 283
6.2.6 Controlled sources.................. 289
6.3 Qualitative properties.................... 293
6.3.1 Equilibria of DC circuits.............. 295
6.3.2 Nonsingularity.................... 297
6.3.3 Hyperbolicity and exponential stability...... 300
xiv Contents
Bibliography 309
Index 325
|
| adam_txt |
Contents
Preface vii
1. Introduction 1
1.1 Historical remarks: Different origins, different names . 2
1.2 DAE analysis. 4
1.2.1 Indices. 5
1.2.2 Dynamics and singularities. 8
1.2.3 Numerical aspects. 10
1.3 State vs. semistate modeling . 11
1.4 Formulations. 12
1.4.1 Input-output descriptions. 13
1.4.2 Leading terms. 15
1.4.3 Semiexplicit, semilinear and quasilinear DAEs . . 16
1.5 Contents and structure of the book. 20
Analytical aspects of DAEs 23
2. Linear DAEs and projector-based methods 25
2.1 Linear time-invariant DAEs. 26
2.1.1 Matrix pencils and the Kronecker canonical form 27
2.1.2 Solving linear time-invariant DAEs via the KCF . 28
2.1.3 A glance at projector-based techniques. 29
2.2 Properly stated linear time-varying DAEs. 35
2.2.1 On standard form index one problems. 36
2.2.2 Properly stated leading terms. 38
2.2.3 P-projectors: Matrix chain and the tractability index 39
2.2.4 The II-framework. 43
2.2.5 Decoupling. 51
2.2.6 A tutorial example . 65
2.2.7 Regular points. 74
xii Contents
2.3 Standard form linear DAEs. 75
2.3.1 The tractability index of standard form DAEs . . 75
2.3.2 Decoupling. 78
2.3.3 Time-invariant problems revisited. 79
2.4 Other approaches for linear DAEs: Reduction techniques 81
3. Nonlinear DAEs and reduction methods 83
3.1 Semiexplicit index one DAEs. 85
3.2 Hessenberg systems. 88
3.3 Some notions from differential geometry. 90
3.4 Quasilinear DAEs: The geometric index. 93
3.4.1 The framework of Rabier and Rheinboldt. 94
3.4.2 Index zero and index one points. 97
3.4.3 Higher index points. 103
3.4.4 Manifold sequences and locally regular DAEs . . . 108
3.4.5 Local equivalence. Ill
3.4.6 Examples. 118
3.4.7 Nonautonomous problems . 123
3.5 Dynamical aspects. 130
3.6 Reduction methods for fully nonlinear DAEs . 133
3.7 The differentiation index and derivative arrays. 134
4. Singularities 137
4.1 What is a singular DAE? . 137
4.2 Singularities of properly stated linear time-varying DAEs 139
4.2.1 Classification of singular points . 140
4.2.2 Decoupling. 145
4.3 Singularities of standard form linear time-varying DAEs . 154
4.3.1 Classification. 154
4.3.2 Decoupling. 156
4.3.3 Analytic problems. 157
4.4 Singularities of autonomous quasilinear DAEs. 160
4.4.1 Quasilinear ODEs and impasse phenomena . 162
4.4.2 Singular points of quasilinear DAEs. 168
4.4.3 A reduction framework for singular problems . 171
4.4.4 Dynamical aspects. 179
4.4.5 Singular semiexplicit index one DAEs. 181
4.4.6 Examples. 184
Contents xiii
Semistate models of electrical circuits 191
5. Nodal analysis 193
5.1 Background on graphs and electrical circuits. 195
5.1.1 Graphs and digraphs. 196
5.1.2 Elementary aspects of circuit theory. 203
5.2 Formulation of nodal models . 212
5.2.1 Node Tableau Analysis. 213
5.2.2 Augmented Nodal Analysis. 214
5.2.3 Modified Nodal Analysis. 215
5.3 Index analysis: Fundamentals. 216
5.3.1 Structural form of nodal models. 216
5.3.2 On the tractability index of quasilinear DAEs . . 218
5.4 Index analysis: Passive circuits. 219
5.4.1 Tableau equations and Augmented Nodal Analysis 220
5.4.2 Modified Nodal Analysis. 232
5.5 Index analysis: Tree methods for non-passive circuits . . . 236
5.5.1 Augmented Nodal Analysis . 237
5.5.2 Modified Nodal Analysis. 243
6. Branch-oriented methods 255
6.1 Branch-oriented semistate models. 257
6.1.1 The basic model. 258
6.1.2 Tree-based formulations. 259
6.1.3 The state formulation problem. 262
6.2 Geometric index analysis and reduction of branch models 264
6.2.1 Operating points. 265
6.2.2 Implicitly described resistors and strict passivity . 265
6.2.3 Multiport reduction. 271
6.2.4 Index characterization. 279
6.2.5 State space reduction. 283
6.2.6 Controlled sources. 289
6.3 Qualitative properties. 293
6.3.1 Equilibria of DC circuits. 295
6.3.2 Nonsingularity. 297
6.3.3 Hyperbolicity and exponential stability. 300
xiv Contents
Bibliography 309
Index 325 |
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| isbn | 9812791809 9789812791801 |
| language | English |
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| spelling | Riaza, Ricardo Verfasser aut Differential algebraic systems analytical aspects and circuit applications Ricardo Riaza Hackensack, NJ [u.a.] World Scientific 2008 XIV, 330 S. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Differential-algebraic equations Electric circuits Mathematical models Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016556824&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Riaza, Ricardo Differential algebraic systems analytical aspects and circuit applications Mathematisches Modell Differential-algebraic equations Electric circuits Mathematical models Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| subject_GND | (DE-588)4229517-8 |
| title | Differential algebraic systems analytical aspects and circuit applications |
| title_auth | Differential algebraic systems analytical aspects and circuit applications |
| title_exact_search | Differential algebraic systems analytical aspects and circuit applications |
| title_exact_search_txtP | Differential algebraic systems analytical aspects and circuit applications |
| title_full | Differential algebraic systems analytical aspects and circuit applications Ricardo Riaza |
| title_fullStr | Differential algebraic systems analytical aspects and circuit applications Ricardo Riaza |
| title_full_unstemmed | Differential algebraic systems analytical aspects and circuit applications Ricardo Riaza |
| title_short | Differential algebraic systems |
| title_sort | differential algebraic systems analytical aspects and circuit applications |
| title_sub | analytical aspects and circuit applications |
| topic | Mathematisches Modell Differential-algebraic equations Electric circuits Mathematical models Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| topic_facet | Mathematisches Modell Differential-algebraic equations Electric circuits Mathematical models Differential-algebraisches Gleichungssystem |
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