Stability In Terms Of Two Measures For Perturbed Dynamic Systems On Time Scales

This dissertation is composed of three chapters and mainly investigates the stability in terms of two measures of several perturbed differential systems on time scales.1. Stability and strict stability in terms of two measures of perturbed differential system.2. Stability and strict stability in terms of two measures of perturbed impulsive differential system with fixed times.3. Practical stability in terms of two measures of perturbed impulsive hybrid differential system.In chapter one, the history of the study about stability of differential systems is introduced accompanied with some prints of present work as well as the practical and theoretical values of this paper. And we also introduce a new framework which many literate are interested in—time scale. All the work in this paper is evolved on time scales.In chapter two, by using the comparison theorem and a family of variation of Lyapunov functions, the nonuniform stability in terms of two measures of the perturbed differential system is discussed. Then we also discuss the uniformly asymptotical stability of the perturbed differential system in virtue of single variation of Lyapunov function and the strict stability in terms of two measures of the comparison system.In chapter three, the stability in terms of two measures of the perturbed impulsive differential system with fixed times is considered. With the use of variation of Lyapunov function and the comparison principle of impulsive differential system, we give some stability criteria for the perturbed impulsive differential system with fixed times. But with respect of system with variable moments of impulsive effect offer more difficult problems compared to the systems with fixed moments of impulsive effect. We will consider about it at the successive work.Chapter four is based on the contents in chapter three. We discuss a special but important case of impulsive differential systems with variable structure—impulsive hybrid differential system. This chapter is composed of two sections. In the first section, we mainly consider the practical stability in terms of two measures of the unperturbed...