Linear multivariable control: a geometric approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
1979
|
| Edition: | 2. ed. |
| Series: | Applications of mathematics
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 326 S. graph. Darst. |
| ISBN: | 3540903542 |
Staff View
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| 245 | 1 | 0 | |a Linear multivariable control |b a geometric approach |c Walter Murray Wonham |
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Record in the Search Index
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| adam_text |
Titel: Linear multivariable control
Autor: Wonham, Walter Murray
Jahr: 1979
Contents Chapter 0 Mathematical Preliminaries 1 0.1 Notation 1 0.2 Linear Spaces 1 0.3 Subspaces 3 0.4 Maps and Matrices 6 0.5 Factor Spaces 9 0.6 Commutative Diagrams 11 0.7 Invariant Subspaces. Induced Maps 12 0.8 Characteristic Polynomial. Spectrum 13 0.9 Polynomial Rings 14 0.10 Rational Canonical Structure 15 0.11 Jordan Decomposition 18 0.12 Dual Spaces 21 0.13 Tensor Product. The Sylvester Map 23 0.14 Inner Product Spaces 25 0.15 Hermitian and Symmetric Maps 26 0.16 Well-Posedness and Genericity 28 0.17 Linear Systems 30 0.18 Transfer Matrices. Signal Flow Graphs 31 0.19 Rouche’s Theorem 32 0.20 Exercises 33 0.21 Notes and References 35 Chapter 1 Introduction to Controllability 36 1.1 Reachability 36 1.2 Controllability 38
Contents xii 1.3 Single-Input Systems 40 1.4 Multi-Input Systems 41 1.5 Controllability is Generic 44 1.6 Exercises 45 1.7 Notes and References 47 Chapter 2 Controllability, Feedback and Pole Assignment 48 2.1 Controllability and Feedback 48 2.2 Pole Assignment 50 2.3 Incomplete Controllability and Pole Shifting 51 2.4 Stabilizability 54 2.5 Exercises 54 2.6 Notes and References 55 Chapter 3 Observability and Dynamic Observers 57 3.1 Observability 57 3.2 Unobservable Subspace 59 3.3 Full Order Dynamic Observer 60 3.4 Minimal Order Dynamic Observer 61 3.5 Observers and Pole Shifting 64 3.6 Detectability 66 3.7 Detectors and Pole Shifting 68 3.8 Pole Shifting by Dynamic Compensation 72 3.9 Observer for a Single Linear Functional 77 3.10 Preservation of Observability and Detectability 79 3.11 Exercises 80 3.12 Notes and References 84 Chapter 4 Disturbance Decoupling and Output Stabilization 86 4.1 Disturbance Decoupling Problem (DDP) 86 4.2 (A, B)-Invariant Subspaces 87 4.3 Solution of DDP 90 4.4 Output Stabilization Problem (OSP) 92 4.5 Exercises 97 4.6 Notes and References 101 Chapter 5 Controllability Subspaces 102 5.1 Controllability Subspaces 5.2 Spectral Assignability 103 105
Contents Xlll 5.3 Controllability Subspace Algorithm 106 5.4 Supremal Controllability Subspace 108 5.5 Transmission Zeros 112 5.6 Disturbance Decoupling with Stability 113 5.7 Controllability Indices 116 5.8 Exercises 122 5.9 Notes and References 128 Chapter 6 Tracking and Regulation I: Output Regulation 129 6.1 Restricted Regulator Problem (RRP) 131 6.2 Solvability of RRP 133 6.3 Extended Regulator Problem (ERP) 138 6.4 Example 142 6.5 Concluding Remarks 144 6.6 Exercises 145 6.7 Notes and References 145 Chapter 7 Tracking and Regulation II: Output Regulation with Internal Stability 146 7.1 Solvability of RPIS: General Considerations 148 7.2 Constructive Solution of RPIS: Jf = 0 151 7.3 Constructive Solution of RPIS: Jf Arbitrary 157 7.4 Application: Regulation Against Step Disturbances 161 7.5 Application: Static Decoupling 162 7.6 Example 1: RPIS Unsolvable 163 7.7 Example 2: Servo-Regulator 165 7.8 Exercises 169 7.9 Notes and References 177 Chapter 8 Tracking and Regulation III: Structurally Stable Synthesis 178 8.1 Preliminaries 178 8.2 Example 1: Structural Stability 180 8.3 Well-Posedness and Genericity 182 8.4 Well-Posedness and Transmission Zeros 185 8.5 Example 2: RPIS Solvable but Ill-Posed 190 8.6 Structurally Stable Synthesis 192 8.7 Example 3: Well-Posed RPIS: Strong Synthesis 201 8.8 The Internal Model Principle 203 8.9 Exercises 210 8.10 Notes and References 213
xiv Contents Chapter 9 Noninteracting Control I: Basic Principles 215 9.1 Decoupling: Systems Formulation 216 9.2 Restricted Decoupling Problem (RDP) 217 9.3 Solution of RDP: Outputs Complete 219 9.4 Extended Decoupling Problem (EDP) 220 9.5 Solution of EDP 222 9.6 Naive Extension 226 9.7 Example 228 9.8 Partial Decoupling 229 9.9 Exercises 230 9.10 Notes and References 233 Chapter 10 Noninteracting Control II: Efficient Compensation 234 10.1 The Radical 234 10.2 Efficient Extension 238 10.3 Efficient Decoupling 242 10.4 Minimal Order Compensation: d(£8) = 2 246 10.5 Minimal Order Compensation: d{2$) = k 251 10.6 Exercises 254 10.7 Notes and References 256 Chapter 11 Noninteracting Control III: Generic Solvability 257 11.1 Generic Solvability of EDP 257 11.2 State Space Extension Bounds 264 11.3 Significance of Generic Solvability 268 11.4 Exercises 269 11.5 Notes and References 269 Chapter 12 Quadratic Optimization I: Existence and Uniqueness 270 12.1 Quadratic Optimization 270 12.2 Dynamic Programming: Heuristics 271 12.3 Dynamic Programming: Rigor 273 12.4 Matrix Quadratic Equation 277 12.5 Exercises 280 12.6 Notes and References 282
Contents XV Chapter 13 Quadratic Optimization II: Dynamic Response 284 13.1 Dynamic Response: Generalities 284 13.2 Example 1: First-Order System 285 13.3 Example 2: Second-Order System 285 13.4 Hamiltonian Matrix 287 13.5 Asymptotic Root Locus: Single Input System 288 13.6 Asymptotic Root Locus: Multivariable System 292 13.7 Upper and Lower Bounds on P° 296 13.8 Stability Margin. Gain Margin 297 13.9 Return Difference Relations 298 13.10 Applicability of Quadratic Optimization 301 13.11 Exercises 301 13.12 Notes and References 303 References 305 Index Relational and Operational Symbols 317 Letter Symbols 319 Synthesis Problems 321 Subject Index 322 |
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| dewey-ones | 629 - Other branches of engineering |
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| dewey-sort | 3629.8 3312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Wirtschaftswissenschaften Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed. |
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| isbn | 3540903542 |
| language | English |
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| physical | XV, 326 S. graph. Darst. |
| publishDate | 1979 |
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| series | Applications of mathematics |
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| spelling | Wonham, Walter Murray 1934-2023 Verfasser (DE-588)172457181 aut Linear multivariable control a geometric approach Walter Murray Wonham 2. ed. Berlin Springer 1979 XV, 326 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 10 Algèbre linéaire Commande, Théorie de la algèbre linéaire commande linéaire commande multivariable contrôlabilité optimisation quadratique théorie commande Algebras, Linear Control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 Multivariate Analyse (DE-588)4040708-1 s 1\p DE-604 Applications of mathematics 10 (DE-604)BV000895226 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001276400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wonham, Walter Murray 1934-2023 Linear multivariable control a geometric approach Applications of mathematics Algèbre linéaire Commande, Théorie de la algèbre linéaire commande linéaire commande multivariable contrôlabilité optimisation quadratique théorie commande Algebras, Linear Control theory Kontrolltheorie (DE-588)4032317-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4040708-1 |
| title | Linear multivariable control a geometric approach |
| title_auth | Linear multivariable control a geometric approach |
| title_exact_search | Linear multivariable control a geometric approach |
| title_full | Linear multivariable control a geometric approach Walter Murray Wonham |
| title_fullStr | Linear multivariable control a geometric approach Walter Murray Wonham |
| title_full_unstemmed | Linear multivariable control a geometric approach Walter Murray Wonham |
| title_short | Linear multivariable control |
| title_sort | linear multivariable control a geometric approach |
| title_sub | a geometric approach |
| topic | Algèbre linéaire Commande, Théorie de la algèbre linéaire commande linéaire commande multivariable contrôlabilité optimisation quadratique théorie commande Algebras, Linear Control theory Kontrolltheorie (DE-588)4032317-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Algèbre linéaire Commande, Théorie de la algèbre linéaire commande linéaire commande multivariable contrôlabilité optimisation quadratique théorie commande Algebras, Linear Control theory Kontrolltheorie Multivariate Analyse |
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