Introduction

Abstract

In engineering, discontinuous dynamical systems exist everywhere. One usually uses continuous models to describe discontinuous dynamical systems. However such continuous models cannot provide suitable predictions of discontinuous dynamical systems. To better understand discontinuous systems, one should realize that discontinuous models will provide an adequate and real predication of engineering systems. Thus, one considers a global discontinuous system consisting of many continuous sub-systems in different domains. For each continuous subsystem, it possesses dynamical properties different from the adjacent continuous subsystems, Because of such difference between two adjacent subsystems, the switch ability and/or transport laws on their boundaries should be addressed. The investigation on such discontinuous systems mainly focused on the time-independent boundary between two dynamical systems. In fact, the boundary relative to time is more popular. In this book, discontinuous dynamical systems on time-varying domains will be of great interest. A brief survey will be given through two practical examples. Finally, the book layout will be presented, and the summarization of all chapters of the main body of this book will be given.KeywordsPeriodic MotionDiscontinuous SystemDiscontinuous BoundaryPiecewise Linear SystemImpact OscillatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.