Verfügbarkeit: Qualitative theory of dynamical systems

Qualitative theory of dynamical systems: the role of stability preserving mappings

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Bibliographische Detailangaben
Beteiligte Personen:	Michel, Anthony N. 1935- (VerfasserIn), Wang, Kaining (VerfasserIn), Hu, Bo (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Dekker 2001
Ausgabe:	2. ed., rev. and expanded
Schriftenreihe:	Pure and applied mathematics 239
Schlagwörter:	Dinâmica topológica Dynamique différentiable Sistemas dinâmicos Differentiable dynamical systems Dynamisches System Ljapunov-Stabilitätstheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009456432&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 707 S. graph. Darst.
ISBN:	0824705262

Internformat

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Datensatz im Suchindex

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adam_text	QUALITATIVE THEORY OF DYNAMICAL SYSTEMS THE ROLE OF STABILITY PRESERVING MAPPINGS SECOND EDITION, REVISED AND EXPANDED ANTHONY N. MICHEL UNIVERSITY OF NOTRE DAME NOTRE DAME, INDIANA KAINING WANG HUBSTORM CORPORATION CUPERTINO, CALIFORNIA BOHU UNIVERSITY OF NOTRE DAME NOTRE DAME, INDIANA / MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE TO THE SECOND EDITION III PREFACE TO THE FIRST EDITION VII 1. INTRODUCTION 1 1.1 DYNAMICAL SYSTEMS 3 1.2 STABILITY PRESERVING MAPPINGS 8 1.3 STABILITY OF MOTION 16 1.4 FINITE DIMENSIONAL SYSTEMS 25 1.5 INFINITE DIMENSIONAL SYSTEMS 26 1.6 DIFFERENTIAL INCLUSIONS 7 27 1.7 HYBRID DYNAMICAL SYSTEMS 28 1.8 STABILITY OF HYBRID AND DISCONTINUOUS DYNAMICAL SYSTEMS 30 1.9 CASE STUDIES IN HYBRID AND DISCONTINUOUS DYNAMICAL SYSTEMS 36 BIBLIOGRAPHY 39 2. DYNAMICAL SYSTEMS 41 2;1 NOTATION 42 2.2 DYNAMICAL SYSTEMS 43 2.3 ORDINARY DIFFERENTIAL EQUATIONS 45 2.4 ORDINARY DIFFERENCE EQUATIONS 55 2.5 ORDINARY DIFFERENTIAL INEQUALITIES 58 2.6 ORDINARY DIFFERENCE INEQUALITIES 60 2.7 FUNCTIONAL DIFFERENTIAL EQUATIONS 61 2.8 VOLTERRA INTEGRODIFFERENTIAL EQUATIONS 70 2.9 SEMIGROUPS 74 2.10 PARTIAL DIFFERENTIAL EQUATIONS . 84 XI XII CONTENTS 2.11 NOTES AND REFERENCES 93 2.12 PROBLEMS 95 BIBLIOGRAPHY 105 3. STABILITY PRESERVING MAPPINGS 111 3.1 INVARIANT SETS 112 3.2 QUALITATIVE CHARACTERIZATIONS 117 3.3 STABILITY PRESERVING MAPPINGS 125 3.4 COMPARISON THEOREMS 134 3.5 APPLICATIONS 140 3.6 A PERSPECTIVE 148 3.7 NOTES AND REFERENCES 150 3.8 PROBLEMS 151 BIBLIOGRAPHY 161 4. STABILITY OF MOTION 165 4.1 SYSTEMS OF DIFFERENTIAL AND DIFFERENCE INEQUALITIES AS COMPARISON SYSTEMS 167 4.2 RESULTS INVOLVING QUASIMONOTONICITY CONDITIONS: CONTINUOUS-TIME CASE 173 4.3 RESULTS INVOLVING MONOTONICITY CONDITIONS: DISCRETE-TIME CASE 181 4.4 THE PRINCIPAL LYAPUNOV THEOREMS FOR GENERAL DYNAMICAL SYSTEMS 185 4.5 CONVERSE THEOREMS 196 4.6 AUTONOMOUS SYSTEMS 205 4.7 INVARIANCE THEORY 209 4.8 UNIQUENESS OF MOTIONS 215 4.9 LYAPUNOV FUNCTIONS AND STABILITY PRESERVING MAPPINGS 220 4.10 APPLICATIONS TO DISCRETE EVENT SYSTEMS 223 4.11 NOTES AND REFERENCES 240 4.12 PROBLEMS 241 BIBLIOGRAPHY 254 5. FINITE DIMENSIONAL SYSTEMS 259 5.1 PRELIMINARIES 260 CONTENTS XIII 5.2 STABILITY AND BOUNDEDNESS 265 5.3 INSTABILITY 274 5.4 INVARIANCE THEORY 278 5.5 CONVERSE THEOREMS 282 5.6 COMPARISON THEORY 284 5.7 APPLICATIONS: ABSOLUTE STABILITY OF REGULATOR SYSTEMS 288 5.8 APPLICATIONS TO ARTIFICIAL NEURAL NETWORKS 295 5.9 APPLICATIONS TO DIGITAL FILTERS 301 5.10 NOTES AND REFERENCES 305 5.11 PROBLEMS 307 BIBLIOGRAPHY 327 6. INFINITE DIMENSIONAL SYSTEMS 333 6.1 PRELIMINARIES 334 6.2 STABILITY AND BOUNDEDNESS 339 6.3 INSTABILITY 351 6.4 INVARIANCE THEORY 359 6.5 CONVERSE THEOREMS 365 6.6 COMPARISON THEORY 366 6.7 HYBRID SYSTEMS 375 6.8 AN APPLICATION TO ARTIFICIAL NEURAL NETWORKS WITH TIME DELAYS 382 6.9 APPLICATION TO A MULTICORE NUCLEAR REACTOR MODEL 387 6.10 NOTES AND REFERENCES 390 6.11 PROBLEMS 391 BIBLIOGRAPHY 406 7. DIFFERENTIAL INCLUSIONS 411 7.1 PRELIMINARIES 413 7.2 STABILITY ANALYSIS 415 7.3 INVARIANCE THEORY 418 7.4 DYNAMICAL SYSTEMS DETERMINED BY DIFFERENTIAL INEQUALITIES 422 7.5 APPLICATIONS TO ROBUST STABILITY 426 XIV CONTENTS 7.6 APPLICATIONS TO ABSOLUTE STABILITY OF REGULATOR SYSTEMS 434 7.7 APPLICATIONS TO A CLASS OF NONLINEAR CIRCUITS AND ARTIFICIAL NEURAL NETWORKS 439 7.8 NOTES AND REFERENCES 445 7.9 PROBLEMS 446 BIBLIOGRAPHY 453 8. HYBRID DYNAMICAL SYSTEMS 457 8.1 A MODEL FOR GENERAL HYBRID DYNAMICAL SYSTEMS 460 8.2 SOME EXAMPLES OF HYBRID DYNAMICAL SYSTEMS DEFINED ON GENERALIZED TIME 463 8.3 SOME QUALITATIVE CHARACTERIZATIONS OF HYBRID DYNAMICAL SYSTEMS 469 8.4 EMBEDDING OF HYBRID DYNAMICAL SYSTEMS INTO DYNAMICAL SYSTEMS DEFINED ON REAL TIME R + 474 8.5 SOME EXAMPLES OF HYBRID DYNAMICAL SYSTEMS DEFINED ON R + 481 8.6 NOTES AND REFERENCES 495 8.7 PROBLEMS 496 BIBLIOGRAPHY 503 9. STABILITY OF HYBRID AND DISCONTINUOUS DYNAMICAL SYSTEMS 509 9.1 STABILITY OF DISCONTINUOUS DYNAMICAL SYSTEMS: RESULTS INVOLVING STABILITY PRESERVING MAPPINGS 510 9.2 THE PRINCIPAL LYAPUNOV THEOREMS FOR DISCONTINUOUS DYNAMICAL SYSTEMS 519 9.3 CONVERSE THEOREMS 540 9.4 RESULTS INVOLVING VECTOR LYAPUNOV FUNCTIONS 555 9.5 INTERCONNECTED SYSTEMS 565 9.6 NOTES AND REFERENCES 573 9.7 PROBLEMS 574 BIBLIOGRAPHY 576 CONTENTS XV 10. CASE STUDIES IN HYBRID AND DISCONTINUOUS DYNAMICAL SYSTEMS 583 10.1 SOME QUALITATIVE PROPERTIES OF SAMPLED-DATA CONTROL SYSTEMS 585 10.2 STABILITY ANALYSIS OF MULTIRATE DIGITAL CONTROL SYSTEMS 597 10.3 STABILITY ANALYSIS OF PULSE-WIDTH-MODULATED FEEDBACK CONTROL SYSTEMS 610 10.4 A CLASS OF VARIABLE STRUCTURE SYSTEMS: HOPFIELD NEURAL NETS WITH INFINITE GAIN AMPLIFIERS ... 638 10.5 DYNAMICAL SYSTEMS SUBJECTED TO STATE SATURATION CONSTRAINTS 659 10.6 NOTES AND REFERENCES 685 BIBLIOGRAPHY 687 INDEX 697
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author	Michel, Anthony N. 1935- Wang, Kaining Hu, Bo
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indexdate	2024-12-20T10:54:14Z
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isbn	0824705262
language	English
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series	Pure and applied mathematics
series2	Pure and applied mathematics
spellingShingle	Michel, Anthony N. 1935- Wang, Kaining Hu, Bo Qualitative theory of dynamical systems the role of stability preserving mappings Pure and applied mathematics Dinâmica topológica larpcal Dynamique différentiable Sistemas dinâmicos larpcal Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd
subject_GND	(DE-588)4013396-5 (DE-588)4167992-1
title	Qualitative theory of dynamical systems the role of stability preserving mappings
title_auth	Qualitative theory of dynamical systems the role of stability preserving mappings
title_exact_search	Qualitative theory of dynamical systems the role of stability preserving mappings
title_full	Qualitative theory of dynamical systems the role of stability preserving mappings Anthony N. Michel ; Kaining Wang ; Bo Hu
title_fullStr	Qualitative theory of dynamical systems the role of stability preserving mappings Anthony N. Michel ; Kaining Wang ; Bo Hu
title_full_unstemmed	Qualitative theory of dynamical systems the role of stability preserving mappings Anthony N. Michel ; Kaining Wang ; Bo Hu
title_short	Qualitative theory of dynamical systems
title_sort	qualitative theory of dynamical systems the role of stability preserving mappings
title_sub	the role of stability preserving mappings
topic	Dinâmica topológica larpcal Dynamique différentiable Sistemas dinâmicos larpcal Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd
topic_facet	Dinâmica topológica Dynamique différentiable Sistemas dinâmicos Differentiable dynamical systems Dynamisches System Ljapunov-Stabilitätstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009456432&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001885
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