Publisher's Synopsis
This book provides a self-contained account of the underlying ideas of a new and important mathematical area which has many applications. To the publisher's knowledge, there is no other book which covers this area. Dynamical systems are subject to impulse effects if the time derivatives of the variables undergo discontinuities in some regular fashion. Such systems provide models for rapidly changing evolution processes, and have innumerable applications to scientific fields such as control theory, population dynamics, mechanics, engineering, and electronics.;The theory of systems with impulse effect has strong analogies with that of ordinary dynamical systems, and the concepts used to analyze stability are generalizations of familiar ideas from dynamical systems theory. The first chapter presents the basic notions and some auxiliary results required later. The second chapter contains results connected with the application of the first method of Lyapunov. The third chapter exploits the direct method of Lyapunov, and introduces specially designed functions analagous to Lyapunov functions. The theory is developed in full analytic rigour, and is illustrated by numerous examples and applications.
