Stability Analysis Of Discontinuous Dynamical Systems And Its Applications

This paper is concerned with stability of several class of discontinuous systems,i.e., impulsive differential systems, impulsive difference system, stochastic differencesystem and impulsive switching system, and its applications on impulsive fuzzy neuralnetworks and chaos synchronization.In Chapter 1, the exponential stability of several impulsive differential systemsis concerned. Sufficient conditions on exponential stability of impulsive singulardifferential equations, impulsive reaction-diffusion equations and impulsive integro-differential equations are obtained, respectively.In Chapter 2, by using a delay difference inequality and the property ofρ?cone,we study the exponential stability of impulsive delay difference equation. Sufficientconditions for exponential stability in mean square of stochastic difference equationare obtained.In Chapter 3, the global impulsive exponential synchronization problem for delaycoupled chaotic systems is investigated. By establishing an impulsive delay differ-ential inequality and using the property of P-cone and unidirectional linear couplingapproach, some simple sufficient conditions for global impulsive exponential synchro-nization of two coupled chaotic systems are derived.In Chapter 4, a new class of switching system with impulses and variable delaysis introduced and their asymptotic stability properties are investigated. By the propertyof negative definite matrix, the state-space is divided into m subregions and then theconstruction of switching regions, called ??i regions, is given. In term of these ??i regions, a switching law is designed. Using the given switching law and an impulsivedelay differential inequality, some general criteria for stability of the switching systemwith impulses and variable delays are given.In Chapter 5, first, a modified stochastic Takagi-Sugeno (TS) fuzzy model is es-tablished. By establishing an impulse fuzzy delay differential inequality, some criteriafor the global exponential stability in the mean square for the modified stochastic TSmodel are obtained. Then sufficient conditions for exponential stability for fuzzy cel-lular neural networks with impulse effect are given.