Stability of dynamical systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2007
|
| Edition: | 1. ed. |
| Series: | Monograph series on nonlinear science and complexity
5 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 671 - 696 |
| Physical Description: | XII, 706 S. graph. Darst. |
| ISBN: | 0444531106 9780444531100 |
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| 245 | 1 | 0 | |a Stability of dynamical systems |c Xiaoxin Liao ; Liqiu Wang ; Pei Yu |
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| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2007 | |
| 300 | |a XII, 706 S. |b graph. Darst. | ||
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| 700 | 1 | |a Yu, Pei |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | STABILITY OF DYNAMICAL SYSTEMS XIAOXIN LIAO HUAZHONG UNIVERSITY OF
SCIENCE AND TECHNOLOGY WUHAN 430074 CHINA LIQIUWANG THE UNIVERSITY OF
HONG KONG HONG KONG HONG KONG PEIYU THE UNIVERSITY OF WESTERN ONTARIO
LONDON, ONTARIO CANADA ELSEVIER AMSTERDAM * BOSTON -HEIDELBERG * LONDON
* NEW YORK *OXFORD PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE *
SYDNEY * TOKYO CONTENTS PREFACE V CHAPTER 1. FUNDAMENTAL CONCEPTS AND
MATHEMATICAL TOOLS 1 1.1. FUNDAMENTAL THEOREMS OF ORDINARY DIFFERENTIAL
EQUATIONS 1 1.2. LYAPUNOV FUNCTION 4 1.3. A -CLASS FUNCTION 7 : 1.4.
DINI DERIVATIVE 10 1.5. DIFFERENTIAL AND INTEGRAL INEQUALITIES 13 1.6. A
UNIFIED SIMPLE CONDITION FOR STABLE MATRIX, P.D. MATRIX AND M MA- TRIX
16 *1.7. DEFINITION OF LYAPUNOV STABILITY 21 1.8. SOME EXAMPLES OF
STABILITY RELATION 24 CHAPTER 2. LINEAR SYSTEMS WITH CONSTANT
COEFFICIENTS 35 , 2.1. NASCS FOR STABILITY AND ASYMPTOTIC STABILITY 35
2.2. SUFFICIENT CONDITIONS OF HURWITZ MATRIX 43 2.3. A NEW METHOD FOR
SOLVING LYAPUNOV MATRIX EQUATION: BA+A T B = C 53 2.4. A SIMPLE
GEOMETRICAL NASC FOR HURWITZ MATRIX 61 2.5. THE GEOMETRY METHOD FOR THE
STABILITY OF LINEAR CONTROL SYSTEMS 69 CHAPTER 3. TIME-VARYING LINEAR
SYSTEMS 77 3.1. STABILITIES BETWEEN HOMOGENEOUS AND NONHOMOGENEOUS
SYSTEMS 77 3.2. EQUIVALENT CONDITION FOR THE STABILITY OF LINEAR SYSTEMS
80 3.3. ROBUST STABILITY OF LINEAR SYSTEMS 84 3.4. THE EXPRESSION OF
CAUCHY MATRIX SOLUTION 90 3.5. LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS
95 3.6. SPECTRAL ESTIMATION FOR LINEAR SYSTEMS 100 : 3.7. PARTIAL
VARIABLE STABILITY OF LINEAR SYSTEMS 104 X CONTENTS CHAPTER 4. LYAPUNOV
DIRECT METHOD 111 4.1. GEOMETRICAL ILLUSTRATION OF LYAPUNOV DIRECT
METHOD 112 4.2. NASCS FOR STABILITY AND UNIFORM STABILITY 113 4.3. NASCS
FOR UNIFORMLY ASYMPTOTIC AND EQUI-ASYMPTOTIC STABILITIES 119 4.4. NASCS
OF EXPONENTIAL STABILITY AND INSTABILITY 127 4.5. SUFFICIENT CONDITIONS
FOR STABILITY 130 4.6. SUFFICIENT CONDITIONS FOR ASYMPTOTIC STABILITY
139 4.7. SUFFICIENT CONDITIONS FOR INSTABILITY 152 4.8. SUMMARY OF
CONSTRUCTING LYAPUNOV FUNCTIONS 162 CHAPTER 5. DEVELOPMENT OF LYAPUNOV
DIRECT METHOD 167 5.1. LASALLE S INVARIANT PRINCIPLE 167 5.2.
COMPARABILITY THEORY 171 5.3. LAGRANGE STABILITY 177 5.4. LAGRANGE
ASYMPTOTIC STABILITY 185 5.5. LAGRANGE EXPONENTIAL STABILITY OF THE
LORENZ SYSTEM 188 5.6. ROBUST STABILITY UNDER DISTURBANCE OF SYSTEM
STRUCTURE 196 5.7. PRACTICAL STABILITY 200 5.8. LIPSCHITZ STABILITY 203
5.9. ASYMPTOTIC EQUIVALENCE OF TWO DYNAMICAL SYSTEMS 208 5.10.
CONDITIONAL STABILITY 218 5.11. PARTIAL VARIABLE STABILITY 224 5.12.
STABILITY AND BOUNDEDNESS OF SETS 235 CHAPTER 6. NONLINEAR SYSTEMS WITH
SEPARATE VARIABLES 241 6.1. LINEAR LYAPUNOV FUNCTION METHOD 241 6.2.
GENERAL NONLINEAR LYAPUNOV FUNCTION WITH SEPARABLE VARIABLE 253 6.3.
SYSTEMS WHICH CAN BE TRANSFORMED TO SEPARABLE VARIABLE SYSTEMS 263 6.4.
PARTIAL VARIABLE STABILITY FOR SYSTEMS WITH SEPARABLE VARIABLES 268 6.5.
AUTONOMOUS SYSTEMS WITH GENERALIZED SEPARABLE VARIABLES 278 6.6.
NONAUTONOMOUS SYSTEMS WITH SEPARABLE VARIABLES 280 CHAPTER 7. ITERATION
METHOD FOR STABILITY 285 7.1. PICARD ITERATION TYPE METHOD 285 7.2.
GAUSS-SEIDEL TYPE ITERATION METHOD 290 CONTENTS XI 7.3. APPLICATION OF
ITERATION METHOD TO EXTREME STABILITY 302 7.4. APPLICATION OF ITERATION
METHOD TO STATIONARY OSCILLATION 307 7.5. APPLICATION OF ITERATION
METHOD TO IMPROVE FROZEN COEFFICIENT METHOD 309 7.6. APPLICATION OF
ITERATION METHOD TO INTERVAL MATRIX 315 CHAPTER 8. DYNAMICAL SYSTEMS
WITH TIME DELAY 321 8.1. BASIC CONCEPTS , 321 8.2. LYAPUNOV FUNCTION
METHOD FOR STABILITY Y ,.- 324 8.3. LYAPUNOV FUNCTION METHOD WITH
RAZUMIKHIN TECHNIQUE 330 8.4. LYAPUNOV FUNCTIONAL METHOD FOR STABILITY
ANALYSIS 338 8.5. NONLINEAR AUTONOMOUS SYSTEMS WITH VARIOUS TIME DELAYS
341 8.6. APPLICATION OF INEQUALITY WITH TIME DELAY AND COMPARISON
PRINCIPLE 350 8.7. ALGEBRAIC METHOD FOR LDS WITH CONSTANT COEFFICIENTS
AND TIME DELAY 356 8.8. A CLASS OF TIME DELAY NEUTRAL DIFFERENTIAL
DIFFERENCE SYSTEMS 362 8.9. THE METHOD OF ITERATION BY PARTS FOR
LARGE-SCALE NEURAL SYSTEMS 366 8.10. STABILITY OF LARGE-SCALE NEUTRAL
SYSTEMS ON C SPACE 373 8.11. ALGEBRAIC METHODS FOR GLNS WITH CONSTANT
COEFFICIENTS 378 CHAPTER 9. ABSOLUTE STABILITY OF NONLINEAR CONTROL
SYSTEMS 389 Y . 9.1. THE PRINCIPAL OF CENTRIFUGAL GOVERNOR AND GENERAL
LURIE SYSTEMS 389 9.2. LYAPUNOV-LURIE TYPE V FUNCTION METHOD 394 9.3.
NASCS OF NEGATIVE DEFINITE FOR DERIVATIVE OF LYAPUNOV-LURIE TYPE
FUNCTION 399 9.4. POPOV S CRITERION AND IMPROVED CRITERION 402 9.5.
SIMPLE ALGEBRAIC CRITERION 407 9.6. NASCS OF ABSOLUTE STABILITY FOR
INDIRECT CONTROL SYSTEMS 420 9.7. NASCS OF ABSOLUTE STABILITY FOR DIRECT
AND CRITICAL CONTROL SYSTEM 434 9.8. NASCS OF ABSOLUTE STABILITY FOR
CONTROL SYSTEMS WITH MULTIPLE NON- LINEAR CONTROLS 442 9.9. NASCS OF
ABSOLUTE STABILITY FOR SYSTEMS WITH FEEDBACK LOOPS 454 9.10. CHAOS
SYNCHRONIZATION AS A STABILIZATION PROBLEM OF LURIE SYSTEM 459 9.11.
NASCS FOR ABSOLUTE STABILITY OF TIME-DELAYED LURIE CONTROL SYSTEMS 469
CHAPTER 10. STABILITY OF NEURAL NETWORKS 487 10.1. HOPFIELD ENERGY
FUNCTION METHOD 487 XII CONTENTS 10.2. LAGRANGE GLOBALLY EXPONENTIAL
STABILITY OF GENERAL NEURAL NETWORK 491 10.3. EXTENSION OF HOPFIELD
ENERGY FUNCTION METHOD 493 10.4. GLOBALLY EXPONENTIAL STABILITY OF
HOPFIELD NEURAL NETWORK 502 10.5. GLOBALLY ASYMPTOTIC STABILITY OF A
CLASS OF HOPFIELD NEURAL NETWORKS 515 10.6. STABILITY OF BIDIRECTIONAL
ASSOCIATIVE MEMORY NEURAL NETWORK 530 10.7. STABILITY OF BAM NEURAL
NETWORKS WITH VARIABLE DELAYS 534 10.8. EXP. STABILITY AND EXP.
PERIODICITY OF DNN WITH LIPSCHITZ TYPE AC- TIVATION FUNCTION 541 10.9.
STABILITY OF GENERAL ECOLOGICAL SYSTEMS AND NEURAL NETWORKS 550 10.10.
CELLULAR NEURAL NETWORK 563 CHAPTER 11. LIMIT CYCLE, NORMAL FORM AND
HOPF BIFURCATION CONTROL 591 11.1. INTRODUCTION 591 11.2. COMPUTATION OF
NORMAL FORMS AND FOCUS VALUES 594 11.2.1 THE TAKENS METHOD 594 11.2.2 A
PERTURBATION METHOD 597 11.2.3 THE SINGULAR POINT VALUE METHOD 599
11.2.4 APPLICATIONS 602 11.3. COMPUTATION OF THE SNF WITH PARAMETERS 613
11.3.1 GENERAL FORMULATION 614 11.3.2 THE SNF FOR SINGLE ZERO 622 11.3.3
THE SNF FOR HOPF BIFURCATION 624 11.4. HOPF BIFURCATION CONTROL 626
11.4.1 CONTINUOUS-TIME SYSTEMS 627 11.4.2 DISCRETE MAPS 640 11.4.3 2-D
LIFTING SURFACE 658 REFERENCES 67 1 SUBJECT INDEX 697
|
| any_adam_object | 1 |
| author | Liao, Xiaoxin Wang, Liqiu Yu, Pei |
| author_facet | Liao, Xiaoxin Wang, Liqiu Yu, Pei |
| author_role | aut aut aut |
| author_sort | Liao, Xiaoxin |
| author_variant | x l xl l w lw p y py |
| building | Verbundindex |
| bvnumber | BV025485833 |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)255735811 (DE-599)BVBBV025485833 |
| dewey-full | 515.392 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.392 |
| dewey-search | 515.392 |
| dewey-sort | 3515.392 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV025485833 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:35:09Z |
| institution | BVB |
| isbn | 0444531106 9780444531100 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020099113 |
| oclc_num | 255735811 |
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| owner_facet | DE-11 |
| physical | XII, 706 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| series | Monograph series on nonlinear science and complexity |
| series2 | Monograph series on nonlinear science and complexity |
| spelling | Liao, Xiaoxin Verfasser aut Stability of dynamical systems Xiaoxin Liao ; Liqiu Wang ; Pei Yu 1. ed. Amsterdam [u.a.] Elsevier 2007 XII, 706 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monograph series on nonlinear science and complexity 5 Literaturverz. S. 671 - 696 Wang, Liqiu Verfasser aut Yu, Pei Verfasser aut Monograph series on nonlinear science and complexity 5 (DE-604)BV035336549 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020099113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liao, Xiaoxin Wang, Liqiu Yu, Pei Stability of dynamical systems Monograph series on nonlinear science and complexity |
| title | Stability of dynamical systems |
| title_auth | Stability of dynamical systems |
| title_exact_search | Stability of dynamical systems |
| title_full | Stability of dynamical systems Xiaoxin Liao ; Liqiu Wang ; Pei Yu |
| title_fullStr | Stability of dynamical systems Xiaoxin Liao ; Liqiu Wang ; Pei Yu |
| title_full_unstemmed | Stability of dynamical systems Xiaoxin Liao ; Liqiu Wang ; Pei Yu |
| title_short | Stability of dynamical systems |
| title_sort | stability of dynamical systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020099113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035336549 |
| work_keys_str_mv | AT liaoxiaoxin stabilityofdynamicalsystems AT wangliqiu stabilityofdynamicalsystems AT yupei stabilityofdynamicalsystems |