LEADER 05290nam 2200817Ia 450 001 9910454324803321 005 20200520144314.0 010 $a1-281-93440-2 010 $a9786611934408 010 $a981-279-423-9 035 $a(CKB)1000000000537805 035 $a(EBL)1679612 035 $a(OCoLC)879074263 035 $a(SSID)ssj0000250365 035 $a(PQKBManifestationID)11193472 035 $a(PQKBTitleCode)TC0000250365 035 $a(PQKBWorkID)10231614 035 $a(PQKB)10344105 035 $a(MiAaPQ)EBC1679612 035 $a(WSP)00005442 035 $a(Au-PeEL)EBL1679612 035 $a(CaPaEBR)ebr10255675 035 $a(CaONFJC)MIL193440 035 $a(EXLCZ)991000000000537805 100 $a20040708d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStability of stationary sets in control systems with discontinuous nonlinearities$b[electronic resource] /$fV.A. Yakubovich, G.A. Leonov, A. Kh. Gelig 210 $aRiver Edge, NJ $cWorld Scientific$dc2004 215 $a1 online resource (352 p.) 225 1 $aSeries on stability, vibration, and control of systems. Series A ;$vv. 14 300 $aDescription based upon print version of record. 311 $a981-238-719-6 320 $aIncludes bibliographical references (p. 323-332) and index. 327 $aContents ; Preface ; List of Notations ; 1. Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides ; 1.1 Notion of Solution to Differential Equation with Discontinuous Right-Hand Side 327 $a1.1.1 Difficulties encountered in the definition of a solution. Sliding modes 1.1.2 The concept of a solution of a system with discontinuous nonlinearities accepted in this book. Connection with the theory of differential equations with multiple-valued right-hand sides 327 $a1.1.3 Relation to some other definitions of a solution to a system with discontinuous right-hand side 1.1.4 Sliding modes. Extended nonlinearity. Example ; 1.2 Systems of Differential Equations with Multiple-Valued Right-Hand Sides (Differential Inclusions) 327 $a1.2.1 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 1.2.2 ""Extended"" nonlinearities ; 1.2.3 Sliding modes 327 $a1.3 Dichotomy and Stability 1.3.1 Basic definitions ; 1.3.2 Lyapunov-type lemmas ; 2. Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type 327 $a2.1 Algebraic Problems that Occur when Finding Conditions for the Existence of Lyapunov Functions from Some Multiparameter Functional Class. Circle Criterion. Popov Criterion 330 $a This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks 410 0$aSeries on stability, vibration, and control of systems.$nSeries A ;$vv. 14. 606 $aControl theory 606 $aNonlinear control theory 606 $aSet theory 606 $aSystem analysis 606 $aDifferential equations, Nonlinear 606 $aEngineering mathematics 606 $aEngineering systems 608 $aElectronic books. 615 0$aControl theory. 615 0$aNonlinear control theory. 615 0$aSet theory. 615 0$aSystem analysis. 615 0$aDifferential equations, Nonlinear. 615 0$aEngineering mathematics. 615 0$aEngineering systems. 676 $a629.836 700 $aI?Akubovich$b V. A$g(Vladimir Andreevich)$0968834 701 $aLeonov$b G. A$g(Gennadii? Alekseevich)$0909966 701 $aGelig$b Arkadii? Khai?movich$0770714 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454324803321 996 $aStability of stationary sets in control systems with discontinuous nonlinearities$92200981 997 $aUNINA