05290nam 2200817Ia 450 991045432480332120200520144314.01-281-93440-29786611934408981-279-423-9(CKB)1000000000537805(EBL)1679612(OCoLC)879074263(SSID)ssj0000250365(PQKBManifestationID)11193472(PQKBTitleCode)TC0000250365(PQKBWorkID)10231614(PQKB)10344105(MiAaPQ)EBC1679612(WSP)00005442(Au-PeEL)EBL1679612(CaPaEBR)ebr10255675(CaONFJC)MIL193440(EXLCZ)99100000000053780520040708d2004 uy 0engur|n|---|||||txtccrStability of stationary sets in control systems with discontinuous nonlinearities[electronic resource] /V.A. Yakubovich, G.A. Leonov, A. Kh. GeligRiver Edge, NJ World Scientificc20041 online resource (352 p.)Series on stability, vibration, and control of systems. Series A ;v. 14Description based upon print version of record.981-238-719-6 Includes bibliographical references (p. 323-332) and index.Contents ; 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 Side1.1.1 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 sides1.1.3 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)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 1.2.2 ""Extended"" nonlinearities ; 1.2.3 Sliding modes1.3 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 Type2.1 Algebraic Problems that Occur when Finding Conditions for the Existence of Lyapunov Functions from Some Multiparameter Functional Class. Circle Criterion. Popov Criterion 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 networksSeries on stability, vibration, and control of systems.Series A ;v. 14.Control theoryNonlinear control theorySet theorySystem analysisDifferential equations, NonlinearEngineering mathematicsEngineering systemsElectronic books.Control theory.Nonlinear control theory.Set theory.System analysis.Differential equations, Nonlinear.Engineering mathematics.Engineering systems.629.836I͡Akubovich V. A(Vladimir Andreevich)968834Leonov G. A(Gennadiĭ Alekseevich)909966Gelig Arkadiĭ Khaĭmovich770714MiAaPQMiAaPQMiAaPQBOOK9910454324803321Stability of stationary sets in control systems with discontinuous nonlinearities2200981UNINA