Matrix diagonal stability in systems and computation:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 232 - 256 |
| Physical Description: | XIV, 267 S. graph. Darst. |
| ISBN: | 3764340886 0817640886 |
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Record in the Search Index
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| adam_text | IMAGE 1
EUGENIUS KASZKUREWICZ
AMIT BHAYA
MATRIX DIAGONAL STABILITY IN SYSTEMS AND COMPUTATION
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE XI
1 DIAGONALLY STABLE STRUCTURES IN SYSTEMS AND COMPUTATION 1
1.1 INTRODUCTION 1
1.2 ROBUST STABILITY OF A MECHANICAL SYSTEM 5
1.3 THE LOTKA-VOLTERRA ECOSYSTEM MODEL 8
1.4 CONVERGENCE OF ASYNCHRONOUS COMPUTATIONS 11
1.5 GLOBAL STABILITY OF NEURAL NETWORKS 15
1.6 VARIABLE STRUCTURE SYSTEMS 17
1.7 EXISTENCE OF DIAGONAL-TYPE LIAPUNOV FUNCTIONS 21
1.8 NOTES AND REFERENCES 23
2 MATRIX DIAGONAL AND D-STABILITY 25
2.1 MATRIX STABILITY CONCEPTS 25
2.1.1 BASIC NOTATION AND TERMINOLOGY 28
2.1.2 BASIC RESULTS ON HURWITZ DIAGONAL AND D-STABILITY 31 2.2 SPECIAL
CLASSES OF HURWITZ DIAGONALLY STABLE MATRICES . 40
2.3 SIMILARITY FOR HURWITZ DIAGONALLY STABLE MATRICES . . .. 46
2.4 PERSISTENCE OF DIAGONAL STABILITY UNDER PERTURBATIONS . . 48
2.5 BASIC RESULTS ON SCHUR DIAGONAL AND D-STABILITY 50
2.6 A MATRIX POLYTOPIC VIEW OF SCHUR DIAGONAL AND D-STABILITY 54 2.7
SPECIAL CLASSES OF SCHUR DIAGONALLY STABLE MATRICES . .. 58
IMAGE 3
VIII CONTENTS
2.7.1 SCHUR DIAGONAL AND D-STABILITY FOR TWO-BY-TWO MATRICES 63
2.7.2 NONNEGATIVE MATRICES 65
2.7.3 QUALITATIVELY SCHUR STABLE MATRICES 72
2.8 TESTING FOR DIAGONAL AND D-STABILITY 75
2.9 NOTES AND REFERENCES 83
2.10 APPENDIX: SUMMARY OF THE THEORY OF THE LIAPUNOV EQUATION 85
3 MATHEMATICAL MODELS ADMITTING DIAGONAL-TYPE LIA PUNOV FUNCTIONS 90
3.1 CLASSES OF NONLINEARITIES AND DIAGONAL-TYPE LIAPUNOV FUNCTIONS 90
3.2 CONTINUOUS-TIME STATE-SPACE MODELS AND STABILITY RESULTS 92 3.3
SEEKING HURWITZ DIAGONAL STABILITY: STATE-SPACE REALIZA-TION PROCEDURES
98
3.4 DISCRETE-TIME STATE-SPACE MODELS AND STABILITY RESULTS 101 3.4.1
DISCRETE-TIME INTERVAL SYSTEMS 108
3.5 MODELS FOR ASYNCHRONOUS SYSTEMS 115
3.6 DISCRETE-TIME SYSTEMS WITH DELAYS 119
3.7 NOTES AND REFERENCES 122
3.8 APPENDIX: SUMMARY OF LIAPUNOV STABILITY THEORY . . .. 123
4 CONVERGENCE OF ASYNCHRONOUS ITERATIVE METHODS 128
4.1 WHAT ARE ASYNCHRONOUS ITERATIVE METHODS? 128
4.2 A MATHEMATICAL MODEL FOR ASYNCHRONOUS BLOCK-ITERATIONS 130 4.2.1
CONVERGENCE CONDITIONS FOR THE ASYNCHRONOUS CASE 133 4.2.2 CONVERGENCE
CONDITIONS FOR THE SYNCHRONOUS CASE 136
4.3 ASYNCHRONOUS ITERATIONS TO SOLVE ALMOST LINEAR EQUATIONS 138 4.4
PARALLEL ASYNCHRONOUS TEAM ALGORITHMS 144
4.5 NOTES AND REFERENCES 152
5 NEURAL NETWORKS, CIRCUITS, AND SYSTEMS 154
5.1 CONTINUOUS-TIME HOPFIELD-TANK NEURAL NETWORKS . . .. 154
5.1.1 A GLOBAL STABILITY RESULT 156
5.1.2 REFINEMENTS OF THE GLOBAL STABILITY RESULT . . .. 158
5.1.3 PERSISTENCE OF GLOBAL ASYMPTOTIC STABILITY . . .. 164
5.2 DISCRETE-TIME NEURAL NETWORKS 166
5.3 PASSIVE RLC CIRCUITS 170
5.4 DIGITAL FILTERS IN STATE-SPACE DESCRIPTION 174
5.5 TWO-DIMENSIONAL (2D) DYNAMICAL SYSTEMS 177
5.6 TROPHIC CHAINS AND COMMUNITIES WITH VERTICAL STRUCTURE 184 5.7 NOTES
AND REFERENCES 190
IMAGE 4
CONTENTS IX
6 INTERCONNECTED SYSTEMS: STABILITY AND STABILIZATION 192
6.1 DIAGONAL STABILITY IN THE LARGE SCALE SYSTEMS APPROACH 192 6.2
ABSOLUTE STABILITY OF INTERCONNECTED SYSTEMS 199
6.3 LINEARLY INTERCONNECTED LUR E SYSTEMS 203
6.4 STABILIZATION BY LINEAR FEEDBACK 210
6.5 DECENTRALIZED POWER-FREQUENCY CONTROL OF POWER SYSTEMS 219 6.6 NOTES
AND REFERENCES 226
6.7 APPENDIX: SUMMARY OF THE LARGE SCALE SYSTEMS APPROACH 227
EPILOGUE 231
REFERENCES 232
INDEX 257
|
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| discipline | Mathematik |
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| isbn | 3764340886 0817640886 |
| language | English |
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| spelling | Kaszkurewicz, Eugenius Verfasser (DE-588)1146241291 aut Matrix diagonal stability in systems and computation Eugenius Kaszkurewicz ; Amit Bhaya Boston [u.a.] Birkhäuser 2000 XIV, 267 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 232 - 256 Differenzierbares dynamisches System - Matrix <Mathematik> - Stabilität Matrizenanalysis (DE-588)4227735-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrizenanalysis (DE-588)4227735-8 s DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s Matrix Mathematik (DE-588)4037968-1 s Stabilität (DE-588)4056693-6 s Bhaya, Amit Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008911022&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaszkurewicz, Eugenius Bhaya, Amit Matrix diagonal stability in systems and computation Differenzierbares dynamisches System - Matrix <Mathematik> - Stabilität Matrizenanalysis (DE-588)4227735-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stabilität (DE-588)4056693-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4227735-8 (DE-588)4137931-7 (DE-588)4056693-6 (DE-588)4037968-1 |
| title | Matrix diagonal stability in systems and computation |
| title_auth | Matrix diagonal stability in systems and computation |
| title_exact_search | Matrix diagonal stability in systems and computation |
| title_full | Matrix diagonal stability in systems and computation Eugenius Kaszkurewicz ; Amit Bhaya |
| title_fullStr | Matrix diagonal stability in systems and computation Eugenius Kaszkurewicz ; Amit Bhaya |
| title_full_unstemmed | Matrix diagonal stability in systems and computation Eugenius Kaszkurewicz ; Amit Bhaya |
| title_short | Matrix diagonal stability in systems and computation |
| title_sort | matrix diagonal stability in systems and computation |
| topic | Differenzierbares dynamisches System - Matrix <Mathematik> - Stabilität Matrizenanalysis (DE-588)4227735-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stabilität (DE-588)4056693-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Differenzierbares dynamisches System - Matrix <Mathematik> - Stabilität Matrizenanalysis Differenzierbares dynamisches System Stabilität Matrix Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008911022&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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