Stability and stabilization of nonlinear systems with random structure:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Taylor & Francis
2002
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| Series: | Stability and control
v. 18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 219-234) and index |
| Physical Description: | xv, 236 p. 26 cm |
| ISBN: | 041527253X |
Staff View
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Record in the Search Index
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| adam_text | STABILITY AND STABILIZATION OF NONLINEAR SYSTEMS WITH RANDOM STRUCTURE
I.YA. KATS URAL ACADEMY OF COMMUNICATION WAYS, YEKATARINBURG, RUSSIA AND
A.A. MARTYNYUK INSTITUTE OF MECHANICS, KIEV, UKRAINE TAYLOR &. FRANCIS
TAYLOR & FRANCIS GROUP LONDON AND NEW YORK CONTENTS INTRODUCTION TO THE
SERIES XI PREFACE XIII 1 PRELIMINARY ANALYSIS 1 1.0 INTRODUCTORY REMARKS
1 1.1 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 2 1.1.1 A
MULTIDIMENSIONAL NORMAL (GAUSSIAN) DISTRIBUTION 4 1.1.2 A POISSON
DISTRIBUTION WITH PARAMETER A 0 5 1.2 PROBABILITY PROCESSES AND THEIR
MATHEMATICAL DESCRIPTION. MARKOV PROCESSES 5 1.3 RANDOM DIFFERENTIAL
EQUATIONS. MODELLING OF SYSTEMS EXPOSED TO RANDOM PERTURBATIONS 10 1.4
SYSTEM WITH RANDOM STRUCTURE. EXAMPLES 14 1.5 COMMENTS AND REFERENCES 22
2 STABILITY ANALYSIS USING SCALAR LYAPUNOV FUNCTIONS 23 2.0 INTRODUCTORY
REMARKS 23 2.1 STABILITY CONCEPTS FOR STOCHASTIC SYSTEMS 24 2.2 RANDOM
SCALAR LYAPUNOV FUNCTIONS 28 VIII CONTENTS 2.3 CONDITIONS OF STABILITY
IN PROBABILITY 34 2.4 CONVERSE THEOREMS 46 2.5 STABILITY IN MEAN SQUARE
52 2.6 STABILITY IN MEAN SQUARE OF LINEAR SYSTEMS 64 2.7 COMMENTS AND
REFERENCES 69 3 STABILITY ANALYSIS USING MULTICOMPONENT LYAPUNOV
FUNCTIONS 73 3.0 INTRODUCTORY REMARKS 73 3.1 VECTOR LYAPUNOV FUNCTIONS
74 3.1.1 A SCALAR APPROACH 75 3.1.2 A VECTOR APPROACH 80 3.2 STOCHASTIC
MATRIX-VALUED LYAPUNOV FUNCTIONS 83 3.2.1 THE STRUCTURE OF AVERAGED
DERIVATIVES OF STOCHASTIC MATRIX-VALUED FUNCTIONS 87 3.3 STABILITY
ANALYSIS IN GENERAL 93 3.4 STABILITY ANALYSIS OF SYSTEMS IN ITO S FORM
95 3.4.1 DECOMPOSITION OF PERTURBED MOTION EQUATIONS 95 3.4.2 THE
STRUCTURE OF AVERAGED DERIVATIVES OF HIERARCHICAL MATRIX-VALUED
FUNCTIONS 98 3.4.3 SUFFICIENT CONDITIONS OF STABILITY IN PROBABILITY OF
A STOCHASTIC ITO SYSTEM 100 3.5 STOCHASTIC SINGULARLY PERTURBED SYSTEMS
104 3.5.1 STATEMENT OF THE PROBLEM AND MAIN DEFINITIONS 104 3.5.2 SMVF
FOR SINGULARLY PERTURBED SYSTEMS 106 3.5.3 THEOREMS ON STABILITY IN THE
WHOLE OF A SINGULARLY PERTURBED SYSTEM 109 3.5.4 A STOCHASTIC LINEAR
AUTONOMOUS SINGULARLY PERTURBED SYSTEM 112 3.6 LARGE-SCALE SINGULARLY
PERTURBED SYSTEMS 117 3.6.1 DESCRIPTION OF THE SYSTEMS 117 3.6.2
INDEPENDENT SUBSYSTEMS 119 3.6.3 STABILITY CONDITIONS FOR STOCHASTIC
SINGULARLY PERTURBED AUTONOMOUS LARGE-SCALE SYSTEMS 120 CONTENTS IX
3.6.4 ANALYSIS OF LINEAR AUTONOMOUS SINGULARLY PERTURBED LARGE-SCALE
SYSTEM 129 3.7 COMMENTS AND REFERENCES 133 4 STABILITY ANALYSIS BY THE
FIRST-ORDER APPROXIMATION 135 4.0 INTRODUCTORY REMARKS 135 4.1 STABILITY
CRITERION BY THE FIRST-ORDER APPROXIMATION 135 4.1.1 ASYMPTOTIC
STABILITY IN PROBABILITY IN THE WHOLE AND EXPONENTIAL STABILITY IN MEAN
SQUARE 135 4.1.2 A SYSTEMS WITH RANDOM STRUCTURE AND SLOWLY-VARYING
RIGHT-HAND SIDES 138 4.2 STABILITY WITH RESPECT TO THE FIRST-ORDER
APPROXIMATION (CONTINUED) 141 4.2.1 THE SYSTEM OF THE FIRST-ORDER
APPROXIMATION WITH CONSTANT STRUCTURE 141 4.2.2 THE SYSTEM OF THE
FIRST-ORDER APPROXIMATION WITH AN UNSTABLE STRUCTURE 144 4.3 STABILITY
BY FIRST-ORDER APPROXIMATION OF SYSTEMS WITH RANDOM DELAY 149 4.4
CONVERGENCE OF STOCHASTIC APPROXIMATION PROCEDURES 156 4.4.1 THE ROBBINS
- MONRO PROCEDURE 156 4.4.2 THE STOCHASTIC PROGRAMMING PROCEDURE 157
4.4.3 THE PROCEDURE OF ESTABLISHING THE ROOT OF AN UNKNOWN FUNCTION 160
4.4.4 TIME-CONTINUOUS MEASUREMENTS IN THE PRESENCE OF RANDOM JUMPS 162
4.5 COMMENTS AND REFERENCES 163 5 STABILIZATION OF CONTROLLED SYSTEMS
WITH RANDOM STRUCTURE 165 5.0 INTRODUCTORY REMARKS 165 5.1 PROBLEMS OF
STABILIZATION 166 5.2 OPTIMAL STABILIZATION 171 5.3 LINEAR-QUADRATIC
OPTIMAL STABILIZATION 175 X CONTENTS 5.4 SUFFICIENT STABILIZATION
CONDITIONS FOR LINEAR SYSTEMS 180 5.5 OPTIMAL SOLUTION EXISTENCE 186 5.6
THE SMALL PARAMETER METHOD ALGORITHM 191 5.7 COMMENTS AND REFERENCES 199
6 APPLICATIONS 201 6.0 INTRODUCTORY REMARKS 201 6.1 A STOCHASTIC VERSION
OF THE LEFSCHETZ PROBLEM 202 6.2 STABILITY IN PROBABILITY OF OSCILLATING
SYSTEMS 204 6.3 STABILITY IN PROBABILITY OF REGULATION SYSTEMS 208 6.4
PRICE STABILITY IN A STOCHASTIC MARKET MODEL 211 6.4.1 A STOCHASTIC
MARKET MODEL 212 6.4.2 A MANAGEMENT PROBLEM BASED ON STABILITY
CONDITIONS 212 6.4.3 ANALYSIS OF STABILITY 213 6.5 COMMENTS AND
REFERENCES 218 REFERENCES 219 INDEX 235
|
| any_adam_object | 1 |
| author | Kats, I. Ya |
| author_facet | Kats, I. Ya |
| author_role | aut |
| author_sort | Kats, I. Ya |
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| bvnumber | BV014560595 |
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| dewey-full | 531.3 |
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| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.3 |
| dewey-search | 531.3 |
| dewey-sort | 3531.3 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV014560595 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:03:32Z |
| institution | BVB |
| isbn | 041527253X |
| language | English |
| lccn | 2002027129 |
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| oclc_num | 248547600 |
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| owner | DE-11 |
| owner_facet | DE-11 |
| physical | xv, 236 p. 26 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Taylor & Francis |
| record_format | marc |
| series2 | Stability and control |
| spelling | Kats, I. Ya Verfasser aut Stability and stabilization of nonlinear systems with random structure I. Ya. Kats, A.A. Martynyuk London Taylor & Francis 2002 xv, 236 p. 26 cm txt rdacontent n rdamedia nc rdacarrier Stability and control v. 18 Includes bibliographical references (p. 219-234) and index Nichtlineare Stabilitätstheorie (DE-588)4171761-2 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtlineare Stabilitätstheorie (DE-588)4171761-2 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Martyniuk, Anatoliĭ Andreevich Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009899229&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kats, I. Ya Stability and stabilization of nonlinear systems with random structure Nichtlineare Stabilitätstheorie (DE-588)4171761-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4171761-2 (DE-588)4167992-1 |
| title | Stability and stabilization of nonlinear systems with random structure |
| title_auth | Stability and stabilization of nonlinear systems with random structure |
| title_exact_search | Stability and stabilization of nonlinear systems with random structure |
| title_full | Stability and stabilization of nonlinear systems with random structure I. Ya. Kats, A.A. Martynyuk |
| title_fullStr | Stability and stabilization of nonlinear systems with random structure I. Ya. Kats, A.A. Martynyuk |
| title_full_unstemmed | Stability and stabilization of nonlinear systems with random structure I. Ya. Kats, A.A. Martynyuk |
| title_short | Stability and stabilization of nonlinear systems with random structure |
| title_sort | stability and stabilization of nonlinear systems with random structure |
| topic | Nichtlineare Stabilitätstheorie (DE-588)4171761-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Nichtlineare Stabilitätstheorie Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009899229&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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