Stability of stationary sets in control systems with discontinuous nonlinearities / V.A. Yakubovich, G.A. Leonov, A. Kh. Gelig.

Format:

Book

Author/Creator:

I︠A︡kubovich, V. A. (Vladimir Andreevich)

Contributor:

Leonov, G. A. (Gennadiĭ Alekseevich)

Gelig, Arkadiĭ Khaĭmovich.

Series:

Series on stability, vibration, and control of systems. Series A ; v. 14.

Series on stability, vibration, and control of systems. Series A ; v. 14

Language:

English

Subjects (All):

Control theory.

Nonlinear control theory.

Set theory.

System analysis.

Differential equations, Nonlinear.

Engineering mathematics.

Engineering systems.

Physical Description:

1 online resource (352 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2004.

Language Note:

English

Summary:

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

Contents:

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 Side

1.1.1 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

1.1.3 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 modes

1.3 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

2.1 Algebraic Problems that Occur when Finding Conditions for the Existence of Lyapunov Functions from Some Multiparameter Functional Class. Circle Criterion. Popov Criterion

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 323-332) and index.

ISBN:

9786611934408

9781281934406

1281934402

9789812794239

9812794239

OCLC:

879074263