Stability And Boundedness Of Some Impulsive Differential Systems

This thesis mainly studies the stability and boundedness of some impulsive differential systems. It is consisted of five chapters.The first chapter is the introduction, which briefly introduces the development history of impulsive differential equations and the research status of impulsive differential systems at home and abroad, as well as the main work of this thesis.In chapter 2, we mainly study the stability and boundedness of the impulsive differential systems which has repeated eigenvalue. By discussing different pulse conditions and through the control of pulse time, we obtain the sufficient conditions for the stablity and boundedness of this system.In chapter 3, we study a simple harmonic oscillator. Under a certain pulse condition, we give the condition that the system still has the periodic solution and the stability.In chapter 4, we study the impulse control problem of a predator-prey system with overcrowding. We impulse control the system via state feedback, by using Lyapunov function and comparison principle, we obtain the sufficient conditions for asymptotic stability under the impulse control.In chapter 5, we make a simple summary for this thesis and point out the deficiency of this thesis as well as prospects for future research.