Matrix Riccati equations in control and systems theory:
Saved in:
| Format: | Book |
|---|---|
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
2012
|
| Edition: | [softcover repr. of the original 1. ed. 2003] |
| Series: | Systems & control: foundations & applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XX, 571 S. |
| ISBN: | 3034894325 9783034894326 |
Staff View
MARC
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| 245 | 1 | 0 | |a Matrix Riccati equations in control and systems theory |c Hisham Abou-Kandil ... |
| 250 | |a [softcover repr. of the original 1. ed. 2003] | ||
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2012 | |
| 300 | |a XX, 571 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Commande, Théorie de la | |
| 650 | 4 | |a Riccati, Équation de | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Riccati equation | |
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| 650 | 0 | 7 | |a Systemtheorie |0 (DE-588)4058812-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xi
Notation
хчі
1 Basic
results for linear equations
і
1.1
Linear differential equations and linear algebraic equations
..... 1
1.2
Exponential dichotomy and L2 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 products 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
Contents
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
4
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 Fréchet
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
5
The periodic Riccati equation
257
5
Л
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-definite periodic equilibria of
PRDE
.......... 279
6
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 Stackelberg
differential games
............................ 322
6.5
Discrete-time open loop Stackelberg 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
Contents ix
7 Symmetrie
differential Riccati equations: an operator based approach
411
7.1
Popov triplets: definition and equivalence
.............. 412
7.2
Associated objects
........................... 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 Stackelberg games
............. 515
9.3.1
Characterization in Hubert space
............... 516
9.3.2
Unique Stackelberg equilibria
................. 517
9.3.3
A value function type approach
................ 520
A Appendix
527
A.I Basic facts from control theory
.................... 527
A.
2
The implicit function theorem
..................... 530
References
533
χ
Contents
Index 569
List of Figures
572
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|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:27Z |
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| isbn | 3034894325 9783034894326 |
| language | German |
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| physical | XX, 571 S. |
| publishDate | 2012 |
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| record_format | marc |
| series2 | Systems & control: foundations & applications |
| spelling | Matrix Riccati equations in control and systems theory Hisham Abou-Kandil ... [softcover repr. of the original 1. ed. 2003] Basel [u.a.] Birkhäuser 2012 XX, 571 S. txt rdacontent n rdamedia nc rdacarrier Systems & control: foundations & applications Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Riccati-Differentialgleichung (DE-588)4230752-1 gnd rswk-swf Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd rswk-swf Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd rswk-swf Systemtheorie (DE-588)4058812-9 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 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027761402&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027761402&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Matrix Riccati equations in control and systems theory Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Kontrolltheorie (DE-588)4032317-1 gnd Riccati-Differentialgleichung (DE-588)4230752-1 gnd Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4230752-1 (DE-588)4434741-8 (DE-588)4434736-4 (DE-588)4058812-9 |
| 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 Kontrolltheorie (DE-588)4032317-1 gnd Riccati-Differentialgleichung (DE-588)4230752-1 gnd Algebraische Riccati-Gleichung (DE-588)4434741-8 gnd Riccati-Matrizendifferentialgleichung (DE-588)4434736-4 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Commande, Théorie de la Riccati, Équation de Control theory Riccati equation Kontrolltheorie Riccati-Differentialgleichung Algebraische Riccati-Gleichung Riccati-Matrizendifferentialgleichung Systemtheorie |
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