Introduction

Abstract

In many control systems, various sudden changes caused by the external surroundings or the internal parameters unavoidably occur during the system operations. The systems with such phenomena can be modeled as switching systems. Conceptually, switching systems commonly consist of a finite number of subsystems (described by differential or difference equations) and an associated switching signal governing the switching among them. The switching signals may belong to a certain set and the set may be various. Note that if the switching signal is autonomous (without designers’ intervention) and a stochastic process can be attached to the switching signal, then the underlying systems are the so-called stochastic switching systems. In the past years, the Markov process or Markov chain has been widely used to describe the switching behaviors, and the corresponding systems are termed as Markov jump systems in the literature. This chapter will give an introduction for this class of dynamic systems.