Stability Analysis Of Hybrid Dynamic Systems

A hybrid dynamic system is a system with different kinds of dynamic ones, which can depict the real-life problems more precisely. As a result, it has vast application on transportation, air tranfic control, engineering and so on. The interesting feature of the set differential equations is that the results obtained in this new framework become the corresponding results of ordinary differential equations as the Hukuhara derivative and the integral used in formulating the set differential equations reduce to the ordinary vector derivative and integral when the set under consideration is a single valued mapping.In this paper, we consider the stability of hybrid dynamic systems and set differential equations. The paper is divided into five chapters and organized as follows:In chapter 1, we sketch the history and development of this problem, involving basic definitions of hybrid system, practical stablity, set differential equation, time scales, etc.. At the end of this chapter we give the brief statement of the main work.There are three sections in chapter 2. Applying Lyapunov functions, comparison theorem and inequality technique, we study the practical stablity andφ0 -stability of discrete hybrid system with initial time difference and establish some sufficient conditions for these two problems, respectively. Besides, the practical stability in terms of two measures of discrete hybrid system is also considered and several new results of the practical stability of the target system are presented.There are two sections in chapter 3. We study the practicalφ0 -stability of nonlinear differential system with initial time difference and impulsive dynamic system with initial time difference, respectively, where the cone-valued Lyapunov functions and comparison theorems are used to get the practicalφ0 -stability criteria for these systems.There are two sections in chapter 4. In section 4.1, we consider the practical stability of set differential equation on time scales, furthermore, we study the practical stability in terms of two measures for set control differential equations or time scales in section 4.2. By using Lyapunov functions, comparison theorem and inequality technique, we obtain the stability criteria for these two classes of equations.