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Series on Stability, Vibration and Control of Systems, Series A - Vol. 14

STABILITY OF STATIONARY SETS IN CONTROL SYSTEMS WITH DISCONTINUOUS NONLINEARITIES

by V A Yakubovich, G A Leonov & A Kh Gelig (Saint Petersburg State University, Russia)

Table of Contents (81k)
Preface (65k)
Chapter 1: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides (455k)

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, phase-locked loops, and synchronous machines.


Contents:

  • Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides
  • Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type
  • Dichotomy and Stability of Nonlinear Systems with Multiple Equilibria
  • Stability of Equilibria Sets of Pendulum-Like Systems


Readership: Upper level undergraduates, graduate students, academics, researchers and engineers involved with mechanics, electrical science and power systems.


“This book is well worth acquiring, not only for reading in English V A Yakubovich explaining the topics which made him famous, but also as a reference for results when this area is extended to differential inclusions.”

Zentralblatt MATH





“... there are many interesting comments and pointers to references concerned with the history of the subject. The main results presented were original contributions of the authors. All topics are closely related to the problem of stability analysis of systems having discontinuous nonlinearities, based on frequency-domain methods ... The reviewer recommends this book: first, to mathematicians interested in control theory and, second, to researchers interested in systems having nonsmooth nonlinearities and their technical applications.” (See Full Review)

IEEE Transactions on Automatic Control




352pp Pub. date: Mar 2004
ISBN 978-981-238-719-6
981-238-719-6
US$98 / £75


Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 5 September 2008