Strict Practical Stability Of Impulsive Differential Systems And Its Application

In this dissertation, we study some strict practical stability properties for two im-pulsive differential systems employing Lyapunov's second method, one system is generic impulsive differential system, the other system is impulsive differential system with per-turbing term.We study the strict practical stability and the strict practical asymptotic stability of impulsive differential systems and impulsive perturbation differential systems by differ-ent approaches in two measures. For example, Lyapunov function, variational Lyapunov function, comparison principle and so on. We also set up some about strictly practical stability and strict practical asymptotic stability criteria.In the front of article we discuss the strict practical stability and the strict practical asymptotic stability of the impulsive differential system in two measures, one part is dis-cussed on the basis of comparison theorem, the other part is only discussed by Lyapunov function. In this part we get stronger result by the weaker conditions. And we give four specific example.In the behind of article we mainly draw support from variational Lyapunov method through without perturbation action of impulsive differential system with two measures to determine the strict practical stability and the strict asymptotic stability of perturbed differential system. One part is discussed on the basis of comparison theorem, the other part is only discussed by variational Lyapunov function. And we give two specific exam-ple. Finally, using a criterion of the second chapter we give the strict practical stability result for microbial batch flow model.