Stability and stabilization: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 457 S. graph. Darst. |
| ISBN: | 0691134448 9780691134444 |
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MARC
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| 100 | 1 | |a Terrell, William J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stability and stabilization |b an introduction |c William J. Terrell |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a XV, 457 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
| _version_ | 1804145698277425152 |
|---|---|
| adam_text | IMAGE 1
LIST OF FIGURES
P. XI
PREFACE
P. XIII
INTRODUCTION
P. 1
OPEN LOOP CONTROL
P. 1
THE FEEDBACK STABILIZATION PROBLEM
P. 2
CHAPTER AND APPENDIX DESCRIPTIONS
P. 5
NOTES AND REFERENCES
P. 11
MATHEMATICAL BACKGROUND
P. 12
ANALYSIS PRELIMINARIES
P. 12
LINEAR ALGEBRA AND MATRIX ALGEBRA
P. 12
MATRIX ANALYSIS
P. 17
ORDINARY DIFFERENTIAL EQUATIONS
P. 30
PHASE PLANE EXAMPLES: LINEAR AND NONLINEAR
P. 35
EXERCISES
P. 44
NOTES AND REFERENCES
P. 48
LINEAR SYSTEMS AND STABILITY
P. 49
THE MATRIX EXPONENTIAL
P. 49
THE PRIMARY DECOMPOSITION AND SOLUTIONS OF LTI SYSTEMS
P. 53
JORDAN FORM AND MATRIX EXPONENTIALS
P. 57
JORDAN FORM OF TWO-DIMENSIONAL SYSTEMS
P. 58
JORDAN FORM OF N-DIMENSIONAL SYSTEMS
P. 61
THE CAYLEY-HAMILTON THEOREM
P. 67
LINEAR TIME VARYING SYSTEMS
P. 68
THE STABILITY DEFINITIONS
P. 71
MOTIVATIONS AND STABILITY DEFINITIONS
P. 71
LYAPUNOV THEORY FOR LINEAR SYSTEMS
P. 73
EXERCISES
P. 77
NOTES AND REFERENCES
P. 81
CONTROLLABILITY OF LINEAR TIME INVARIANT SYSTEMS
P. 82
INTRODUCTION
P. 82
LINEAR EQUIVALENCE OF LINEAR SYSTEMS
P. 84
CONTROLLABILITY WITH SCALAR INPUT
P. 88
EIGENVALUE PLACEMENT WITH SINGLE INPUT
P. 92
CONTROLLABILITY WITH VECTOR INPUT
P. 94
EIGENVALUE PLACEMENT WITH VECTOR INPUT
P. 96
THE PBH CONTROLLABILITY TEST
P. 99
LINEAR TIME VARYING SYSTEMS: AN EXAMPLE
P. 103
EXERCISES
P. 105
NOTES AND REFERENCES
P. 108
OBSERVABILITY AND DUALITY
P. 109
OBSERVABILITY, DUALITY, AND A NORMAL FORM
P. 109
IMAGE 2
LYAPUNOV EQUATIONS AND HURWITZ MATRICES
P. 117
THE PBH OBSERVABILITY TEST
P. 118
EXERCISES
P. 121
NOTES AND REFERENCES
P. 123
STABILIZABILITY OF LTI SYSTEMS
P. 124
STABILIZING FEEDBACKS FOR CONTROLLABLE SYSTEMS
P. 124
LIMITATIONS ON EIGENVALUE PLACEMENT
P. 128
THE PBH STABILIZABILITY TEST
P. 133
EXERCISES
P. 134
NOTES AND REFERENCES
P. 136
DETECTABILITY AND DUALITY
P. 138
AN EXAMPLE OF AN OBSERVER SYSTEM
P. 138
DETECTABILITY, THE PBH TEST, AND DUALITY
P. 142
OBSERVER-BASED DYNAMIC STABILIZATION
P. 145
LINEAR DYNAMIC CONTROLLERS AND STABILIZERS
P. 147
LQR AND THE ALGEBRAIC RICCATI EQUATION
P. 152
EXERCISES
P. 156
NOTES AND REFERENCES
P. 159
STABILITY THEORY
P. 161
LYAPUNOV THEOREMS AND LINEARIZATION
P. 161
LYAPUNOV THEOREMS
P. 162
STABILIZATION FROM THE JACOBIAN LINEARIZATION
P. 171
BROCKETT S NECESSARY CONDITION
P. 172
EXAMPLES OF CRITICAL PROBLEMS
P. 173
THE INVARIANCE THEOREM
P. 176
BASIN OF ATTRACTION
P. 181
CONVERSE LYAPUNOV THEOREMS
P. 183
EXERCISES
P. 183
NOTES AND REFERENCES
P. 187
CASCADE SYSTEMS
P. 189
THE THEOREM ON TOTAL STABILITY
P. 189
LYAPUNOV STABILITY IN CASCADE SYSTEMS
P. 192
ASYMPTOTIC STABILITY IN CASCADES
P. 193
EXAMPLES OF PLANAR SYSTEMS
P. 193
BOUNDEDNESS OF DRIVEN TRAJECTORIES
P. 196
LOCAL ASYMPTOTIC STABILITY
P. 199
BOUNDEDNESS AND GLOBAL ASYMPTOTIC STABILITY
P. 202
CASCADES BY AGGREGATION
P. 204
APPENDIX: THE POINCARN++E-BENDIXSON THEOREM
P. 207
EXERCISES
P. 207
NOTES AND REFERENCES
P. 211
IMAGE 3
CENTER MANIFOLD THEORY
P. 212
INTRODUCTION
P. 212
AN EXAMPLE
P. 212
INVARIANT MANIFOLDS
P. 213
SPECIAL COORDINATES FOR CRITICAL PROBLEMS
P. 214
THE MAIN THEOREMS
P. 215
DEFINITION AND EXISTENCE OF CENTER MANIFOLDS
P. 215
THE REDUCED DYNAMICS
P. 218
APPROXIMATION OF A CENTER MANIFOLD
P. 222
TWO APPLICATIONS
P. 225
ADDING AN INTEGRATOR FOR STABILIZATION
P. 226
LAS IN SPECIAL CASCADES: CENTER MANIFOLD ARGUMENT
P. 228
EXERCISES
P. 229
NOTES AND REFERENCES
P. 231
ZERO DYNAMICS
P. 233
THE RELATIVE DEGREE AND NORMAL FORM
P. 233
THE ZERO DYNA
TABLE OF CONTENTS PROVIDED BY BLACKWELL S BOOK SERVICES AND R.R. BOWKER.
USED WITH PERMISSION.
|
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| author_facet | Terrell, William J. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:23:35Z |
| institution | BVB |
| isbn | 0691134448 9780691134444 |
| language | English |
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| physical | XV, 457 S. graph. Darst. |
| publishDate | 2009 |
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| spelling | Terrell, William J. Verfasser aut Stability and stabilization an introduction William J. Terrell Princeton, NJ [u.a.] Princeton Univ. Press 2009 XV, 457 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Stabilität (DE-588)4056693-6 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s Stabilität (DE-588)4056693-6 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022556525&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Terrell, William J. Stability and stabilization an introduction Stabilität (DE-588)4056693-6 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4116671-1 |
| title | Stability and stabilization an introduction |
| title_auth | Stability and stabilization an introduction |
| title_exact_search | Stability and stabilization an introduction |
| title_full | Stability and stabilization an introduction William J. Terrell |
| title_fullStr | Stability and stabilization an introduction William J. Terrell |
| title_full_unstemmed | Stability and stabilization an introduction William J. Terrell |
| title_short | Stability and stabilization |
| title_sort | stability and stabilization an introduction |
| title_sub | an introduction |
| topic | Stabilität (DE-588)4056693-6 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd |
| topic_facet | Stabilität System von gewöhnlichen Differentialgleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022556525&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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