1.

Record Nr.

UNINA9910454324803321

Autore

I͡Akubovich V. A (Vladimir Andreevich)

Titolo

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

Pubbl/distr/stampa

River Edge, NJ, : World Scientific, c2004

ISBN

1-281-93440-2

9786611934408

981-279-423-9

Descrizione fisica

1 online resource (352 p.)

Collana

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

Altri autori (Persone)

LeonovG. A (Gennadiĭ Alekseevich)

GeligArkadiĭ Khaĭmovich

Disciplina

629.836

Soggetti

Control theory

Nonlinear control theory

Set theory

System analysis

Differential equations, Nonlinear

Engineering mathematics

Engineering systems

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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

Sommario/riassunto

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