A course in robust control theory: a convex approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Texts in applied mathematics
36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 399 - 409 |
| Physical Description: | XX, 417 S. graph. Darst. : 24 cm |
| ISBN: | 0387989455 |
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Record in the Search Index
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| adam_text | GEIR E. DULLERUD FERNANDO PAGANINI A COURSE IN ROBUST CONTROL THEORY A
CONVEX APPROACH WITH 36 ILLUSTRATIONS SPRINGER CONTENTS SERIES PREFACE
VII PREFACE IX FIGURES XIX 0 INTRODUCTION 1 0.1 SYSTEM REPRESENTATIONS 2
0.1.1 BLOCK DIAGRAMS 2 0.1.2 NONLINEAR EQUATIONS AND LINEAR
DECOMPOSITIONS . . 4 0.2 ROBUST CONTROL PROBLEMS AND UNCERTAINTY 9 0.2.1
STABILIZATION 9 0.2.2 DISTURBANCES AND COMMANDS 12 0.2.3 UNMODELED
DYNAMICS 15 NOTES AND REFERENCES 17 1 PRELIMINARIES IN FINITE
DIMENSIONAL SPACE 19 1.1 LINEAR SPACES AND MAPPINGS 19 1.1.1 VECTOR
SPACES 20 1.1.2 SUBSPACES 23 1.1.3 BASES, SPANS, AND LINEAR INDEPENDENCE
23 1.1.4 MAPPINGS AND MATRIX REPRESENTATIONS 25 1.1.5 CHANGE OF BASIS
AND IN VARIANCE 29 1.2 SUBSETS AND CONVEXITY 31 XIV CONTENTS 1.2.1 SOME
BASIC TOPOLOGY 32 1.2.2 CONVEX SETS 33 1.3 MATRIX THEORY 40 1.3.1
EIGENVALUES AND JORDAN FORM 40 1.3.2 SELF-ADJOINT, UNITARY, AND POSITIVE
DEFINITE MATRICES 43 1.3.3 SINGULAR VALUE DECOMPOSITION 47 1.4 LINEAR
MATRIX INEQUALITIES 49 EXERCISES 55 NOTES AND REFERENCES 58 2 STATE
SPACE SYSTEM THEORY 59 2.1 THE AUTONOMOUS SYSTEM 60 2.2 CONTROLLABILITY
63 2.2.1 REACHABILITY 63 2.2.2 PROPERTIES OF CONTROLLABILITY 68 2.2.3
STABILIZABILITY 71 2.2.4 CONTROLLABILITY FROM A SINGLE INPUT 74 2.3
EIGENVALUE ASSIGNMENT 76 2.3.1 SINGLE-INPUT CASE 76 2.3.2 MULTI-INPUT
CASE 77 2.4 OBSERVABILITY 80 2.4.1 THE UNOBSERVABLE SUBSPACE 80 2.4.2
OBSERVERS 83 2.4.3 OBSERVER-BASED CONTROLLERS 85 2.5 MINIMAL
REALIZATIONS 86 2.6 TRANSFER FUNCTIONS AND STATE SPACE 89 2.6.1 RATIONAL
MATRICES AND STATE SPACE REALIZATIONS . . 92 2.6.2 MINIMALITY 94
EXERCISES 96 NOTES AND REFERENCES 100 3 LINEAR ANALYSIS 101 3.1 NORMED
AND INNER PRODUCT SPACES 102 3.1.1 COMPLETE SPACES 105 3.2 OPERATORS 107
3.2.1 BANACH ALGEBRAS 109 3.2.2 SOME ELEMENTS OF SPECTRAL THEORY 112
3.2.3 ADJOINT OPERATORS IN HILBERT SPACE 115 3.3 FREQUENCY DOMAIN
SPACES: SIGNALS 117 3.3.1 THE SPACE L% AND THE FOURIER TRANSFORM 117
3.3.2 THE SPACES HI AND H^~ AND THE LAPLACE TRANSFORM 119 3.3.3
SUMMARIZING THE BIG PICTURE 123 3.4 FREQUENCY DOMAIN SPACES: OPERATORS
124 3.4.1 TIME INVARIANCE AND MULTIPLICATION OPERATORS . . 125 3.4.2
CAUSALITY WITH TIME INVARIANCE 126 CONTENTS XV 3.4.3 CAUSALITY AND H^
128 EXERCISES 131 NOTES AND REFERENCES 134 4 MODEL REALIZATIONS AND
REDUCTION 137 4.1 LYAPUNOV EQUATIONS AND INEQUALITIES 137 4.2
OBSERVABILITY OPERATOR AND GRAMIAN 140 4.3 CONTROLLABILITY OPERATOR AND
GRAMIAN 143 4.4 BALANCED REALIZATIONS 146 4.5 HANKEL OPERATORS 149 4.6
MODEL REDUCTION 153 4.6.1 LIMITATIONS 154 4.6.2 BALANCED TRUNCATION 157
4.6.3 INNER TRANSFER FUNCTIONS 160 4.6.4 BOUND FOR THE BALANCED
TRUNCATION ERROR 161 4.7 GENERALIZED GRAMIANS AND TRUNCATIONS 166
EXERCISES 168 NOTES AND REFERENCES 172 5 STABILIZING CONTROLLERS 173 5.1
SYSTEM STABILITY 175 5.2 STABILIZATION 178 5.2.1 STATIC STATE FEEDBACK
STABILIZATION VIA LMIS . . . 179 5.2.2 AN LMI CHARACTERIZATION OF THE
STABILIZATION PROB- LEM 180 5.3 PARAMETRIZATION OF STABILIZING
CONTROLLERS 182 5.3.1 COPRIME FACTORIZATION 182 5.3.2 CONTROLLER
PARAMETRIZATION 185 5.3.3 CLOSED-LOOP MAPS FOR THE GENERAL SYSTEM 190
EXERCISES 191 NOTES AND REFERENCES 194 6 H 2 OPTIMAL CONTROL 195 6.1
MOTIVATION FOR H 2 CONTROL 197 6.2 RICCATI EQUATION AND HAMILTONIAN
MATRIX 199 6.3 SYNTHESIS 204 6.4 STATE FEEDBACK H 2 SYNTHESIS VIA LMIS
210 EXERCISES 213 NOTES AND REFERENCES 215 7 ILOO SYNTHESIS 217 7.1 TWO
IMPORTANT MATRIX INEQUALITIES 218 7.1.1 THE KALMAN-YAKUBOVICH-POPOV
LEMMA 221 7.2 SYNTHESIS 224 7.3 CONTROLLER RECONSTRUCTION 231 XVI
CONTENTS EXERCISES 232 NOTES AND REFERENCES 235 8 UNCERTAIN SYSTEMS 237
8.1 UNCERTAINTY MODELING AND WELL-CONNECTEDNESS 239 8.2 ARBITRARY
BLOCK-STRUCTURED UNCERTAINTY 245 8.2.1 A SCALED SMALL GAIN TEST AND ITS
SUFFICIENCY . . . . 246 8.2.2 NECESSITY OF THE SCALED SMALL GAIN TEST
249 8.3 THE STRUCTURED SINGULAR VALUE 255 8.4 TIME INVARIANT UNCERTAINTY
259 8.4.1 ANALYSIS OF TIME INVARIANT UNCERTAINTY 260 8.4.2 THE MATRIX
STRUCTURED SINGULAR VALUE AND ITS UPPER BOUND 267 EXERCISES 272 NOTES
AND REFERENCES 278 9 FEEDBACK CONTROL OF UNCERTAIN SYSTEMS 281 9.1
EXTENDED SPACES AND STABILITY 284 9.1.1 A GENERAL RESULT ON STABILITY
286 9.1.2 CAUSALITY AND MAPS ON 2 -EXTENDED 288 9.2 ROBUST STABILITY
AND PERFORMANCE 290 9.2.1 ROBUST STABILITY UNDER ARBITRARY STRUCTURED
UNCER- TAINTY 291 9.2.2 ROBUST STABILITY UNDER LTI UNCERTAINTY 292 9.2.3
ROBUST PERFORMANCE ANALYSIS 292 9.3 ROBUST CONTROLLER SYNTHESIS 294
9.3.1 ROBUST SYNTHESIS AGAINST A 295 9.3.2 ROBUST SYNTHESIS AGAINST ATI
300 9.3.3 D-K ITERATION: A SYNTHESIS HEURISTIC 303 EXERCISES 305 NOTES
AND REFERENCES 307 10 FURTHER TOPICS: ANALYSIS 309 10.1 ANALYSIS VIA
INTEGRAL QUADRATIC CONSTRAINTS 309 10.1.1 ANALYSIS RESULTS 315 10.1.2
THE SEARCH FOR AN APPROPRIATE IQC 320 10.2 ROBUST H 2 PERFORMANCE
ANALYSIS 322 10.2.1 PROBLEM FORMULATION 323 10.2.2 FREQUENCY DOMAIN
METHODS AND THEIR INTERPRETATION 325 10.2.3 STATE SPACE BOUNDS INVOLVING
CAUSALITY 329 10.2.4 DISCUSSION 333 NOTES AND REFERENCES 336 11 FURTHER
TOPICS: SYNTHESIS 339 11.1 LINEAR PARAMETER VARYING AND MULTIDIMENSIONAL
SYSTEMS 340 CONTENTS XVII 11.1.1 LPV SYNTHESIS 344 11.1.2 REALIZATION
THEORY FOR MULTIDIMENSIONAL SYSTEMS . 350 11.2 A FRAMEWORK FOR
TIME-VARYING SYSTEMS: SYNTHESIS AND ANALYSIS 354 11.2.1 MEMORYLESS
TIME-VARYING OPERATORS 356 11.2.2 THE SYSTEM FUNCTION 358 11.2.3
EVALUATING THE L 2 INDUCED NORM 362 11.2.4 LTV SYNTHESIS 366 11.2.5
PERIODIC SYSTEMS AND FINITE DIMENSIONAL CONDITIONS 367 NOTES AND
REFERENCES 369 A SOME BASIC MEASURE THEORY 371 A.I SETS OF ZERO MEASURE
371 A.2 TERMINOLOGY 374 A.3 COMMENTS ON NORMS AND L P SPACES 376 NOTES
AND REFERENCES 377 B PROOFS OF STRICT SEPARATION 379 NOTES AND
REFERENCES 384 C /X-SIMPLE STRUCTURES 385 C.I THE CASE OF A 1?1 386 C.2
THE CASE OF A 0 ] 3 390 NOTES AND REFERENCES 394 NOTATION 395 REFERENCES
399 INDEX 411
|
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| language | English |
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| spelling | Dullerud, Geir E. 1966- Verfasser (DE-588)121988295 aut A course in robust control theory a convex approach Geir E. Dullerud ; Fernando Paganini New York [u.a.] Springer 2000 XX, 417 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 36 Literaturverz. S. 399 - 409 Commande robuste Théorie de la commande Control theory Robust control Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Robuste Kontrolle (DE-588)4232797-0 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Robuste Kontrolle (DE-588)4232797-0 s DE-604 Paganini, Fernando Verfasser aut Texts in applied mathematics 36 (DE-604)BV002476038 36 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008954740&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dullerud, Geir E. 1966- Paganini, Fernando A course in robust control theory a convex approach Texts in applied mathematics Commande robuste Théorie de la commande Control theory Robust control Kontrolltheorie (DE-588)4032317-1 gnd Robuste Kontrolle (DE-588)4232797-0 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4232797-0 |
| title | A course in robust control theory a convex approach |
| title_auth | A course in robust control theory a convex approach |
| title_exact_search | A course in robust control theory a convex approach |
| title_full | A course in robust control theory a convex approach Geir E. Dullerud ; Fernando Paganini |
| title_fullStr | A course in robust control theory a convex approach Geir E. Dullerud ; Fernando Paganini |
| title_full_unstemmed | A course in robust control theory a convex approach Geir E. Dullerud ; Fernando Paganini |
| title_short | A course in robust control theory |
| title_sort | a course in robust control theory a convex approach |
| title_sub | a convex approach |
| topic | Commande robuste Théorie de la commande Control theory Robust control Kontrolltheorie (DE-588)4032317-1 gnd Robuste Kontrolle (DE-588)4232797-0 gnd |
| topic_facet | Commande robuste Théorie de la commande Control theory Robust control Kontrolltheorie Robuste Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008954740&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT dullerudgeire acourseinrobustcontroltheoryaconvexapproach AT paganinifernando acourseinrobustcontroltheoryaconvexapproach |