Stability Analysis For Impulsive Hybrid Dynamic Systems

In this dissertation, different approaches, such as perturbing Lyapunov functions, cone-valued Lyapunov functions, piecewise continuous Lyapunov functions and so on, are employed to study the stability of impulsive hybrid dynamic systems.This dissertation is composed of four chapters.In Chapter 1, the history of the study and some present work on the stability of impulsive hybrid dynamic systems and the main work of this paper are introduced.In Chapter 2, some sufficient conditions are obtained for the relativeΦ0-stability of the two impulsive hybrid systems by using the method of perturbing Lyapunov functions.In Chapter 3, using cone-valued Lyapunov function, the equi-integralΦ0-stability of perturbed system of impulsive hybrid dynamic system is studied.In Chapter 4, criterion of (h0, h)—eventual stablity is established for impulsive hybrid systems by using piecewise continuous Lyapunov functions. An example is discussed to illustrate the theorem.