Frequency domain criteria for absolute stability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Acad. Pr.
1973
|
| Series: | Electrical science.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 246 S. |
| ISBN: | 0125140509 |
Staff View
MARC
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| 245 | 1 | 0 | |a Frequency domain criteria for absolute stability |c Kumpati S. Narendra ; James H. Taylor* |
| 264 | 1 | |a New York |b Acad. Pr. |c 1973 | |
| 300 | |a XVIII, 246 S. | ||
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| 650 | 4 | |a Systèmes, Analyse de | |
| 650 | 7 | |a Systèmes, Analyse de |2 Rameau | |
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Record in the Search Index
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| adam_text | CONTENTS
Foreword xi
Preface xiii
Acknowledgments xv
Special Notation xvii
I. Introduction
1. The System 1
2. Stability of Motion 6
3. Lyapunov s Direct Method 7
4. The Quadratic Lyapunov Function 10
5. Some Problems in Stability 11
6. The Conjectures of Aizerman and Kalman 13
7. The Absolute Stability Problem 14
8. The Criterion of Popov 15
9. Synopsis * 16
II. Problem Statement
1. System Definition 18
2. Definitions of Stability 33
3. Formal Problem Statement 38
III. Mathematical Preliminaries
1. Sufficiency Theorems 40
2. The Absolute Lyapunov Function Candidates 44
vii
yjii Contents
3. Restated Stability Theorems 48
4. The Kalman Yakubovich Lemma 48
5. Positive Real Functions 57
6. Existence Theorems 61
IV. Linear Time Invariant Systems and Absolute Stability
1. Relations between Linear Time Invariant and Nonlinear Time Varying
Systems 67
2. The Existence of the Quadratic Lyapunov Function xTPx and the
Hurwitz Condition 81
3. The Existence of the Quadratic Lyapunov Function xrPx + KxrMx and
the Nyquist Criterion 84
V. Stability of Nonlinear Systems
1. The Popov Stability Criterion 91
2. Stability Criteria for Monotonic Nonlinearities 99
3. Linear Systems 113
4. Odd Monotonic Gains 116
5. The General Finite Sector Problem 118
VI. Stability of Nonlinear Time Varying Systems
1. The Circle Criterion 123
2. An Extension of the Popov Criterion—Point Conditions 126
3. Stability Criteria for Restricted Nonlinear Behavior—Point Conditions 131
4. The Gentral Finite Sector Problem 135
5. Periodic Nonlinear Time Varying Gains 137
6. Extension of the Popov Criterion—Integral Conditions 138
7. Integral Conditions for Restricted Nonlinear and Linear Gains 141
8. Integral Conditions for Linear Time Varying Systems 142
VII. Geometric Stability Criteria
1. Linear Time Invariant Systems 149
2. The Circle Criterion 155
3. The Popov Criterion 158
4. Monotonic Nonlinearities: An Off Axis Circle Criterion 166
5. Further Geometric Interpretations for Time Varying Systems 175
VIII. The Mathien Equation: An Example
1. Solutions of the Mathieu Equation 186
2. Linear Case (a **= 1): A Perturbation Analysis 187
3. Linear Case (a % 4): A Floquet Analysis 189
Contents ix
4. Application of Stability Criteria to the Linear Case 190
5. Application of Stability Criteria to the Nonlinear Case 198
IX. Absolute Stability of Systems with Multiple
Nonlinear Time Varying Gains
1. Introduction 202
2. Problem Statement 203
3. Mathematical Preliminaries 209
4. Linear Time Invariant Systems and Absolute Stability 213
5. Stability of Nonlinear Systems 216
6. Stability of Nonlinear Time Varying Systems 225
APPENDIX. Matrix Version of the Kalman Yakubovich Lemma 230
References 235
Index 243
|
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| id | DE-604.BV002281086 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:18Z |
| institution | BVB |
| isbn | 0125140509 |
| language | English |
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| physical | XVIII, 246 S. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Acad. Pr. |
| record_format | marc |
| series2 | Electrical science. |
| spelling | Narendra, Kumpati S. Verfasser aut Frequency domain criteria for absolute stability Kumpati S. Narendra ; James H. Taylor* New York Acad. Pr. 1973 XVIII, 246 S. txt rdacontent n rdamedia nc rdacarrier Electrical science. Liapounov, Fonctions de Liapounov, Fonctions de Rameau Stabilité Stabilité Rameau Systèmes, Analyse de Systèmes, Analyse de Rameau Lyapunov functions Stability System analysis Stabilität (DE-588)4056693-6 gnd rswk-swf Häufigkeitsbereich gnd rswk-swf Stabilität (DE-588)4056693-6 s Häufigkeitsbereich f DE-604 Taylor, James H. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Narendra, Kumpati S. Taylor, James H. Frequency domain criteria for absolute stability Liapounov, Fonctions de Liapounov, Fonctions de Rameau Stabilité Stabilité Rameau Systèmes, Analyse de Systèmes, Analyse de Rameau Lyapunov functions Stability System analysis Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4056693-6 |
| title | Frequency domain criteria for absolute stability |
| title_auth | Frequency domain criteria for absolute stability |
| title_exact_search | Frequency domain criteria for absolute stability |
| title_full | Frequency domain criteria for absolute stability Kumpati S. Narendra ; James H. Taylor* |
| title_fullStr | Frequency domain criteria for absolute stability Kumpati S. Narendra ; James H. Taylor* |
| title_full_unstemmed | Frequency domain criteria for absolute stability Kumpati S. Narendra ; James H. Taylor* |
| title_short | Frequency domain criteria for absolute stability |
| title_sort | frequency domain criteria for absolute stability |
| topic | Liapounov, Fonctions de Liapounov, Fonctions de Rameau Stabilité Stabilité Rameau Systèmes, Analyse de Systèmes, Analyse de Rameau Lyapunov functions Stability System analysis Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Liapounov, Fonctions de Stabilité Systèmes, Analyse de Lyapunov functions Stability System analysis Stabilität Häufigkeitsbereich |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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