Stability of stationary sets in control systems with discontinuous nonlinearities:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
River Edge, NJ [u.a.]
World Scientific
2004
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| Series: | Series on stability, vibration and control of systems
Series A ; 14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 334 S. graph. Darst. |
| ISBN: | 9812387196 |
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| 245 | 1 | 0 | |a Stability of stationary sets in control systems with discontinuous nonlinearities |c V. A. Yakubovich ; G.A. Leonov ; A. Kh. Gelig |
| 264 | 1 | |a River Edge, NJ [u.a.] |b World Scientific |c 2004 | |
| 300 | |a XV, 334 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| adam_text | SERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS SERIES A VOLUME 14
FOUNDER & EDITOR: ARDESHIR GURAN CO-EDITORS: M. CLOUD & W. B. ZIMMERMAN
STABILITY OF STATIONARY SETS IN CONTROL SYSTEMS WITH DISCONTINUOUS
NONLINEARITIES V. A. YAKUBOVICH G. A. LEONOV A. KH. GELIG ST. PETERSBURG
STATE UNIVERSITY, RUSSIA ** WORLD SCIENTIFIC NEWJERSEY * LONDON *
SINGAPORE * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS PREFACE V
LIST OF NOTATIONS IX 1. FOUNDATIONS OF THEORY OF DIFFERENTIAL EQUATIONS
WITH DIS- CONTINUOUS RIGHT-HAND SIDES 1 1.1 NOTION OF SOLUTION TO
DIFFERENTIAL EQUATION WITH DISCONTINUOUS RIGHT-HAND SIDE 2 1.1.1
DIFFICULTIES ENCOUNTERED IN THE DEFINITION OF A SOLUTION. SLIDING MODES
2 1.1.2 THE CONCEPT OF A SOLUTION OF A SYSTEM WITH DISCON- TINUOUS
NONLINEARITIES ACCEPTED IN THIS BOOK. CON- NECTION WITH THE THEORY OF
DIFFERENTIAL EQUATIONS WITH MULTIPLE-VALUED RIGHT-HAND SIDES 6 1.1.3
RELATION TO SOME OTHER DEFINITIONS OF A SOLUTION TO A SYSTEM WITH
DISCONTINUOUS RIGHT-HAND SIDE 14 1.1.4 SLIDING MODES. EXTENDED
NONLINEARITY. EXAMPLE ... 20 1.2 SYSTEMS OF DIFFERENTIAL EQUATIONS WITH
MULTIPLE-VALUED RIGHT-HAND SIDES (DIFFERENTIAL INCLUSIONS) 26 1.2.1
CONCEPT OF A SOLUTION OF A SYSTEM OF DIFFERENTIAL EQUATIONS WITH A
MULTIVALUED RIGHT-HAND SIDE, THE LOCAL EXISTENCE THEOREM, THE THEOREMS
ON CONTINUATION OF SOLUTIONS AND CONTINUOUS DEPENDENCE ON INITIAL VALUES
27 1.2.2 EXTENDED NONLINEARITIES 37 1.2.3 SLIDING MODES 44 XI XII
STABILITY OF STATIONARY SETS IN CONTROL SYSTEMS WITH DISCONTINUOUS
NONLINEARITIES 1.3 DICHOTOMY AND STABILITY 55 1.3.1 BASIC DEFINITIONS 55
1.3.2 LYAPUNOV-TYPE LEMMAS 57 2. AUXILIARY ALGEBRAIC STATEMENTS ON
SOLUTIONS OF MATRIX INEQUALITIES OF A SPECIAL TYPE 61 2.1 ALGEBRAIC
PROBLEMS THAT OCCUR WHEN FINDING CONDITIONS FOR THE EXISTENCE OF
LYAPUNOV FUNCTIONS FROM SOME MULTIPARAMETER FUNCTIONAL CLASS. CIRCLE
CRITERION. POPOV CRITERION 62 2.1.1 EQUATIONS OF THE SYSTEM. LINEAR AND
NONLINEAR PARTS OF THE SYSTEM. TRANSFER FUNCTION AND FREQUENCY RESPONSE
63 2.1.2 EXISTENCE OF A LYAPUNOV FUNCTION FROM THE CLASS OF QUADRATIC
FORMS. 5-PROCEDURE 64 2.1.3 EXISTENCE OF A LYAPUNOV FUNCTION IN THE
CLASS OF QUADRATIC FORMS (CONTINUED). FREQUENCY-DOMAIN THEOREM 69 2.1.4
THE CIRCLE CRITERION 71 2.1.5 A SYSTEM WITH A STATIONARY NONLINEARITY.
EXISTENCE OF A LYAPUNOV FUNCTION IN THE CLASS A QUADRATIC FORM PLUS AN
INTEGRAL OF THE NONLINEARITY 75 2.1.6 POPOV CRITERION 79 2.2 RELEVANT
ALGEBRAIC STATEMENTS 84 2.2.1 CONTROLLABILITY, OBSERVABILITY, AND
STABILIZABILITY ... 84 2.2.2 FREQUENCY-DOMAIN THEOREM ON SOLUTIONS OF
SOME MA- TRIX INEQUALITIES 91 2.2.3 ADDITIONAL AUXILIARY LEMMAS 101
2.2.4 THE AE-PROCEDURE THEOREM 106 2.2.5 ON THE METHOD OF LINEAR MATRIX
INEQUALITIES IN CONTROL THEORY 109 3. DICHOTOMY AND STABILITY OF
NONLINEAR SYSTEMS WITH MUL- TIPLE EQUILIBRIA 111 3.1 SYSTEMS WITH
PIECEWISE SINGLE-VALUED NONLINEARITIES .... 112 CONTENTS XIII 3.1.1
SYSTEMS WITH SEVERAL NONLINEARITIES. FREQUENCY- DOMAIN CONDITIONS FOR
QUASI-GRADIENT-LIKE BEHAVIOR AND POINTWISE GLOBAL STABILITY. FREE
GYROSCOPE WITH DRY FRICTION 112 3.1.2 THE CASE OF A SINGLE NONLINEARITY
AND DET P * 0. THEO REM 3.4 ON GRADIENT-LIKE BEHAVIOR AND POINTWISE
GLOBAL STABILITY OF THE SEGMENT OF REST. EXAMPLES 120 3.1.3 THE CASE OF
A SINGLE NONLINEARITY AND ONE ZERO POLE OF THE TRANSFER FUNCTION.
THEOREM 3.6 ON QUASI-GRADIENT LIKE BEHAVIOR AND POINTWISE GLOBAL
STABILITY. THE BUL GAKOV PROBLEM 124 3.1.4 THE CASE OF A SINGLE
NONLINEARITY AND DOUBLE ZERO POLE OF THE TRANSFER FUNCTION. THEOREM 3.8
ON GLOBAL STABIL ITY OF THE SEGMENT OF REST. GYROSCOPIC ROLL EQUALIZER.
THE PROBLEM OF LUR E AND POSTNIKOV. CONTROL SYSTEM FOR A TURBINE.
PROBLEM OF AN AUTOPILOT 130 3.2 SYSTEMS WITH MONOTONE PIECEWISE
SINGLE-VALUED NONLINEARITIES 141 3.2.1 SYSTEMS WITH A SINGLE
NONLINEARITY. FREQUENCY-DOMAIN CONDITIONS FOR DICHOTOMY AND GLOBAL
STABILITY. COR RECTED GYROSTABILIZER WITH DRY FRICTION. THE PROBLEM OF
VYSHNEGRADSKII 142 3.2.2 SYSTEMS WITH SEVERAL NONLINEARITIES. FREQUENCY-
DOMAIN CRITERIA FOR DICHOTOMY. NONCORRECTABLE GY ROSTABILIZER WITH DRY
FRICTION 160 3.3 SYSTEMS WITH GRADIENT NONLINEARITIES 167 3.3.1
DICHOTOMY AND QUASI-GRADIENT-LIKENESS OF SYSTEMS WITH GRADIENT
NONLINEARITIES 167 3.3.2 DICHOTOMY AND QUASI-GRADIENT-LIKE BEHAVIOR OF
NONLINEAR ELECTRICAL CIRCUITS AND OF CELLULAR NEURAL NETWORKS 171 4.
STABILITY OF EQUILIBRIA SETS OF PENDULUM-LIKE SYSTEMS 175 4.1
FORMULATION OF THE STABILITY PROBLEM FOR EQUILIBRIUM SETS OF
PENDULUM-LIKE SYSTEMS 175 4.1.1 SPECIAL FEATURES OF THE DYNAMICS OF
PENDULUM-LIKE SYS TEMS. THE STRUCTURE OF THEIR EQUILIBRIA SETS 175
4.1.2 CANONICAL FORMS OF PENDULUM-LIKE SYSTEMS WITH A SIN GLE SCALAR
NONLINEARITY 183 XIV STABILITY OF STATIONARY SETS IN CONTROL SYSTEMS
WITH DISCONTINUOUS NONLINEARITIES 4.1.3 DICHOTOMY. GRADIENT-LIKE
BEHAVIOR IN A CLASS OF NON- LINEARITIES WITH ZERO MEAN VALUE 189 4.2 THE
METHOD OF PERIODIC LYAPUNOV FUNCTIONS 192 4.2.1 THEOREM ON GRADIENT-LIKE
BEHAVIOR 192 4.2.2 PHASE-LOCKED LOOPS WITH FIRST- AND SECOND-ORDER LOW-
PASS FILTERS 201 4.3 AN ANALOGUE OF THE CIRCLE CRITERION FOR
PENDULUM-LIKE SYS- TEMS 203 4.3.1 CRITERION FOR BOUNDEDNESS OF SOLUTIONS
OF PENDULUM- LIKE SYSTEMS 204 4.3.2 LEMMA ON POINTWISE DICHOTOMY 210
4.3.3 STABILITY OF TWO- AND THREE-DIMENSIONAL PENDULUM-LIKE SYSTEMS.
EXAMPLES 212 4.3.4 PHASE-LOCKED LOOPS WITH A BAND AMPLIFIER 216 4.4 THE
METHOD OF NON-LOCAL REDUCTION 218 4.4.1 THE PROPERTIES OF SEPARATRICES
OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM 219 4.4.2 THE THEOREM ON NONLOCAL
REDUCTION 222 4.4.3 THEOREM ON BOUNDEDNESS OF SOLUTIONS AND ON
GRADIENT-LIKE BEHAVIOR 223 4.4.4 GENERALIZED BOEHM-HAYES THEOREM 228
4.4.5 APPROXIMATION OF THE ACQUISITION BANDS OF PHASE- LOCKED LOOPS WITH
VARIOUS LOW-PASS FILTERS 229 4.5 NECESSARY CONDITIONS FOR GRADIENT-LIKE
BEHAVIOR OF PENDULUM-LIKE SYSTEMS 235 4.5.1 CONDITIONS FOR THE EXISTENCE
OF CIRCULAR SOLUTIONS AND CYCLES OF THE SECOND KIND 236 4.5.2
GENERALIZED HAYES THEOREM 244 4.5.3 ESTIMATION OF THE INSTABILITY
REGIONS IN SEARCHING PLL SYSTEMS AND PLL SYSTEMS WITH 1/2 FILTER 245 4.6
STABILITY OF THE DYNAMICAL SYSTEMS DESCRIBING THE SYNCHRONOUS MACHINES
251 4.6.1 FORMULATION OF THE PROBLEM 252 4.6.2 THE CASE OF ZERO LOAD 253
4.6.3 THE CASE OF A NONZERO LOAD 258 5. APPENDIX. PROOFS OF THE THEOREMS
OF CHAPTER 2 269 5.1 PROOFS OF THEOREMS ON CONTROLLABILITY,
OBSERVABILITY, IRREDUCIBILITY, AND OF LEMMAS 2.4 AND 2.7 269 CONTENTS XV
5.1.1 PROOF OF THE EQUIVALENCE OF CONTROLLABILITY TO PROPER- TIES
(I)-(IV) OF THEOREM 2.6 269 5.1.2 PROOF OF THE THEOREM 2.7 273 5.1.3
COMPLETION OF THE PROOF OF THEOREM 2.6 274 5.1.4 PROOF OF THEOREM 2.8
275 5.1.5 PROOF OF THEOREM 2.9 IN THE SCALAR CASE M = I = I . . 275
5.1.6 PROOF OF THEOREM 2.9 FOR THE CASE WHEN EITHER M 1 OR I 1 AND
PROOF OF THEOREM 2.10 277 5.1.7 PROOF OF LEMMA 2.4 279 5.1.8 PROOF OF
LEMMA 2.7 281 5.2 PROOF OF THEOREM 2.13 (NONSINGULAR CASE). THEOREM ON
SOLUTIONS OF LUR E EQUATION (ALGEBRAIC RICCATI EQUATION) . 283 5.2.1 TWO
LEMMAS. A DETAILED VERSION OF FREQUENCY-DOMAIN THEOREM FOR THE
NONSINGULAR CASE 283 5.2.2 PROOF OF THEOREM 5.1. THE THEOREM ON
SOLVABILITY OF THE LUR E EQUATION 289 5.2.3 LEMMA ON J-ORTHOGONALITY OF
THE ROOT SUBSPACES OF A HAMILTONIAN MATRIX 295 5.3 PROOF OF THEOREM 2.13
(COMPLETION) AND LEMMA 5.1 .... 297 5.3.1 PROOF OF LEMMA 5.1 297 5.3.2
PROOF OF THEOREM 2.13 298 5.4 PROOFS OF THEOREMS 2.12 AND 2.14 (SINGULAR
CASE) 301 5.4.1 PROOF OF THEOREM 2.12 301 5.4.2 NECESSITY OF THE
HYPOTHESES OF THEOREM 2.14 306 5.4.3 SUFFICIENCY OF THE HYPOTHESES OF
THEOREM 2.14 . . . . 309 5.5 PROOFS OF THEOREMS 2.17-2.19 ON
LOSSLESSNESS OF 5-PROCEDURE 316 5.5.1 THE DINES THEOREM 316 5.5.2 PROOFS
OF THE THEOREMS ON THE LOSSLESSNESS OF THE S- PROCEDURE FOR QUADRATIC
FORMS AND ONE CONSTRAINT . . 318 BIBLIOGRAPHY 323 INDEX 333
|
| any_adam_object | 1 |
| author | Jakubovič, Vladimir A. Leonov, Gennadij A. 1947- Gelig, Arkadij Ch |
| author_GND | (DE-588)111346487 |
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| isbn | 9812387196 |
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| series | Series on stability, vibration and control of systems |
| series2 | Series on stability, vibration and control of systems : Series A |
| spelling | Jakubovič, Vladimir A. Verfasser aut Stability of stationary sets in control systems with discontinuous nonlinearities V. A. Yakubovich ; G.A. Leonov ; A. Kh. Gelig River Edge, NJ [u.a.] World Scientific 2004 XV, 334 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on stability, vibration and control of systems : Series A 14 Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Nichtlineare Kontrolltheorie (DE-588)4475218-0 s DE-604 Leonov, Gennadij A. 1947- Verfasser (DE-588)111346487 aut Gelig, Arkadij Ch. Verfasser aut Series on stability, vibration and control of systems Series A ; 14 (DE-604)BV013189168 14 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013325416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jakubovič, Vladimir A. Leonov, Gennadij A. 1947- Gelig, Arkadij Ch Stability of stationary sets in control systems with discontinuous nonlinearities Series on stability, vibration and control of systems Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd |
| subject_GND | (DE-588)4475218-0 |
| title | Stability of stationary sets in control systems with discontinuous nonlinearities |
| title_auth | Stability of stationary sets in control systems with discontinuous nonlinearities |
| title_exact_search | Stability of stationary sets in control systems with discontinuous nonlinearities |
| title_full | Stability of stationary sets in control systems with discontinuous nonlinearities V. A. Yakubovich ; G.A. Leonov ; A. Kh. Gelig |
| title_fullStr | Stability of stationary sets in control systems with discontinuous nonlinearities V. A. Yakubovich ; G.A. Leonov ; A. Kh. Gelig |
| title_full_unstemmed | Stability of stationary sets in control systems with discontinuous nonlinearities V. A. Yakubovich ; G.A. Leonov ; A. Kh. Gelig |
| title_short | Stability of stationary sets in control systems with discontinuous nonlinearities |
| title_sort | stability of stationary sets in control systems with discontinuous nonlinearities |
| topic | Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd |
| topic_facet | Nichtlineare Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013325416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013189168 |
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