Matrix Riccati equations in control and systems theory:
Saved in:
| Format: | Book |
|---|---|
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | Systems & control: Foundations & applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 571 S. |
| ISBN: | 376430085X |
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Record in the Search Index
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| adam_text | IMAGE 1
HISHAM ABOU-KANDIL
GERHARD FREILING VLAD IONESCU (T) GERHARD JANK
MATRIX RICCATI EQUATIONS
IN CONTROL AND SYSTEMS THEORY
BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN
IMAGE 2
CONTENTS
PREFACE XI
NOTATION XVI
1 BASIC RESULTS FOR LINEAR EQUATIONS 1
1.1 LINEAR DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRAIC EQUATIONS 1
1.2 EXPONENTIAL DICHOTOMY AND L 2 EVOLUTIONS 11
2 HAMILTONIAN MATRICES AND ALGEBRAIC RICCATI EQUATIONS 21
2.1 SOLUTIONS OF ALGEBRAIC RICCATI EQUATIONS AND GRAPH SUBSPACES . .. 22
2.2 INDEFINITE SCALAR PRODUETS AND A CANONICAL FORM OF HAMILTONIAN
MATRICES 27
2.3 HERMITIAN ALGEBRAIC RICCATI EQUATIONS 50
2.4 POSITIVE SEMI-DEFINITE SOLUTIONS OF STANDARD ALGEBRAIC RICCATI
EQUATIONS 58
2.5 HERMITIAN DISCRETE-TIME ALGEBRAIC RICCATI EQUATIONS 80
3 GLOBAL ASPECTS OF RICCATI DIFFERENTIAL AND DIFFERENCE EQUATIONS 89
3.1 RICCATI DIFFERENTIAL EQUATIONS AND ASSOCIATED LINEAR SYSTEMS 90
3.1.1 RICCATI DIFFERENTIAL EQUATIONS, RICCATI-TRANSFORMATION AND
SPECTRAL FACTORIZATION 92
3.1.2 RICCATI DIFFERENTIAL EQUATIONS AND LINEAR BOUNDARY VALUE PROBLEMS
95
3.2 A REPRESENTATION FORMULA 97
3.3 FLOWS ON GRASSMANN MANIFOLDS: THE EXTENDED RICCATI DIFFERENTIAL
EQUATION 110
3.4 GENERAL REPRESENTATION FORMULAE FOR SOLUTIONS OF RDE AND PRDE, THE
TIME-CONTINUOUS AND PERIODIC RICCATI DIFFERENTIAL EQUATION, AND
DICHOTOMY 133
3.4.1 A GENERAL REPRESENTATION FORMULA FOR SOLUTIONS OF RDE . . . 134
3.4.2 A REPRESENTATION FORMULA FOR SOLUTIONS OF THE PERIODIC RICCATI
DIFFERENTIAL EQUATION PRDE 144
IMAGE 3
3.5 A REPRESENTATION FORMULA FOR SOLUTIONS OF THE DISCRETE TIME RICCATI
EQUATION 150
3.5.1 PROPERTIES OF THE SOLUTIONS TO DARE 156
3.5.2 PROPERTIES OF THE SOLUTIONS TO DRDE 158
3.6 GLOBAL EXISTENCE RESULTS 163
HERMITIAN RICCATI DIFFERENTIAL EQUATIONS 181
4.1 COMPARISON RESULTS FOR HRDE 181
4.1.1 ARBITRARY COEFFICIENTS 181
4.1.2 PERIODIC COEFFICIENTS 188
4.1.3 CONSTANT COEFFICIENTS 189
4.1.4 RICCATI INEQUALITIES 193
4.2 MONOTONICITY AND CONVEXITY RESULTS: A FRECHET DERIVATIVE BASED
APPROACH 198
4.2.1 NOTATION AND PRELIMINARIES 198
4.2.2 RESULTS FOR HARE 202
4.2.3 RESULTS FOR HDARE 206
4.2.4 RESULTS FOR HRDE 207
4.3 CONVERGENCE TO THE SEMI-STABILIZING SOLUTION 209
4.4 DEPENDENCE OF HRDE ON A PARAMETER 220
4.5 AN EXISTENCE THEOREM FOR GENERAL HRDE 239
4.6 A SPECIAL PROPERTY OF HRDE 247
THE PERIODIC RICCATI EQUATION 257
5.1 LINEAR PERIODIC DIFFERENTIAL EQUATIONS 257
5.2 PRELIMINARY NOTATION AND RESULTS FOR LINEAR PERIODIC SYSTEMS . . ..
262 5.3 EXISTENCE RESULTS FOR PERIODIC HERMITIAN RICCATI EQUATIONS 268
5.4 POSITIVE SEMI-DEFLNITE PERIODIC EQUILIBRIA OF PRDE 279
COUPLED AND GENERALIZED RICCATI EQUATIONS 299
6.1 SOME BASIC CONCEPTS IN DYNAMIC GAMES 299
6.2 NON-SYMMETRIC RICCATI EQUATIONS IN OPEN LOOP NASH DIFFERENTIAL GAMES
302
6.3 DISCRETE-TIME OPEN LOOP NASH RICCATI EQUATIONS 313
6.4 NON-SYMMETRIC RICCATI EQUATIONS IN OPEN LOOP STACKEIBERG
DIFFERENTIAL GAMES 322
6.5 DISCRETE-TIME OPEN LOOP STACKEIBERG EQUATIONS 328
6.6 COUPLED RICCATI EQUATIONS IN CLOSED LOOP NASH DIFFERENTIAL GAMES .
333 6.7 RATIONAL MATRIX DIFFERENTIAL EQUATIONS ARISING IN STOCHASTIC
CONTROL. 343 6.8 RATIONAL MATRIX DIFFERENCE EQUATIONS ARISING IN
STOCHASTIC CONTROL . 377 6.9 COUPLED RICCATI EQUATIONS IN MARKOVIAN JUMP
SYSTEMS 394
IMAGE 4
CONTENTS IX
7 SYMMETRIE DIFFERENTIAL RICCATI EQUATIONS: AN OPERATOR BASED APPROACH
411 7.1 POPOV TRIPLETS: DEFMITION AND EQUIVALENCE 412
7.2 ASSOCIATED OBJEETS 413
7.3 ASSOCIATED OPERATORS 422
7.4 EXISTENCE OF THE STABILIZING SOLUTION 428
7.5 POSITIVITY THEORY AND APPLICATIONS 434
7.6 DIFFERENTIAL RICCATI INEQUALITIES 439
7.7 THE SIGNATURE CONDITION 444
7.8 DIFFERENTIAL RICCATI THEORY: A HAMILTONIAN DESCRIPTOR OPERATOR
APPROACH 455
7.8.1 DESCRIPTORS AND DICHOTOMY 455
7.8.2 HAMILTONIAN DESCRIPTORS 461
7.8.3 THE STABILIZING (ANTI-STABILIZING) SOLUTION 463
8 APPLICATIONS TO ROBUST CONTROL SYSTEMS 467
8.1 THE FOUR BLOCK NEHARI PROBLEM 467
8.1.1 PROBLEM STATEMENT 467
8.1.2 A CHARACTERIZATION OF ALL SOLUTIONS 469
8.1.3 MAIN RESULT 471
8.2 DISTURBANCE ATTENUATION 479
8.2.1 PROBLEM STATEMENT 479
8.2.2 A NECESSARY CONDITION 481
8.2.3 THE DISTURBANCE FEEDFORWARD PROBLEM 485
8.2.4 THE LEAST ACHIEVABLE TOLERANCE OF THE DF PROBLEM 490
9 NON-SYMMETRIC RICCATI THEORY AND APPLICATIONS 495
9.1 NON-SYMMETRIC RICCATI THEORY 496
9.1.1 BASIC NOTIONS AND PRELIMINARY RESULTS 496
9.1.2 TOEPLITZ OPERATORS AND RICCATI EQUATIONS 501
9.2 APPLICATION TO OPEN LOOP NASH GAMES 507
9.2.1 DEFINITIONS AND HUBERT SPACE 507
9.2.2 UNIQUE NASH EQUILIBRIA 509
9.2.3 THE GENERAL CASE 512
9.2.4 IF ANY, THEN ONE OR INFINITELY MANY 513
9.3 APPLICATION TO OPEN LOOP STACKEIBERG GAMES 515
9.3.1 CHARACTERIZATION IN HUBERT SPACE 516
9.3.2 UNIQUE STACKEIBERG EQUILIBRIA 517
9.3.3 A VALUE FUNETION TYPE APPROACH 520
A APPENDIX 527
A.L BASIC FACTS FROM CONTROL THEORY 527
A.2 THE IMPLICIT FUNETION THEOREM 530
REFERENCES 533
IMAGE 5
X
CONTENTS
INDEX 569
LIST OF FIGURES 572
|
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| spelling | Matrix Riccati equations in control and systems theory Hisham Abou-Kandil ... Basel [u.a.] Birkhäuser 2003 XX, 571 S. txt rdacontent n rdamedia nc rdacarrier Systems & control: Foundations & applications Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Riccati-Differentialgleichung (DE-588)4230752-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd rswk-swf Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd rswk-swf Algebraische Riccati-Gleichung (DE-588)4434741-8 s DE-604 Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 s Riccati-Differentialgleichung (DE-588)4230752-1 s Kontrolltheorie (DE-588)4032317-1 s Systemtheorie (DE-588)4058812-9 s b DE-604 Abou-Kandil, Hisham 1954- Sonstige (DE-588)113785267 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matrix Riccati equations in control and systems theory Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Riccati-Differentialgleichung (DE-588)4230752-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd |
| subject_GND | (DE-588)4230752-1 (DE-588)4032317-1 (DE-588)4058812-9 (DE-588)4434736-4 (DE-588)4434741-8 |
| title | Matrix Riccati equations in control and systems theory |
| title_auth | Matrix Riccati equations in control and systems theory |
| title_exact_search | Matrix Riccati equations in control and systems theory |
| title_full | Matrix Riccati equations in control and systems theory Hisham Abou-Kandil ... |
| title_fullStr | Matrix Riccati equations in control and systems theory Hisham Abou-Kandil ... |
| title_full_unstemmed | Matrix Riccati equations in control and systems theory Hisham Abou-Kandil ... |
| title_short | Matrix Riccati equations in control and systems theory |
| title_sort | matrix riccati equations in control and systems theory |
| topic | Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Riccati-Differentialgleichung (DE-588)4230752-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd |
| topic_facet | Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Riccati-Differentialgleichung Kontrolltheorie Systemtheorie Riccati-Matrizendifferentialgleichung Algebraische Riccati-Gleichung |
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