Impulse Control Problems For Some Kinds Of Differential Equations

This thesis mainly studies the impulse control problems for some kinds of special differential equations. It is consisted of five chapters.As the introduction, in Chapter1, the background and history of impulsive differential equation and impulse control are briefly addressed, and the main results of this work are stated.In Chapter2, we study the existence of periodic solution for a harvested system, which conforms to the Gompertz growth mode, with impulses at variable times. By using the qualitative theory of differential system with depend on the state of the pulse, we obtain the sufficient and necessary conditions for the existence and uniqueness of periodic solution of the system.In Chapter3, we consider the impulse control problem of a predator-prey system with functional reaction function by using the comparison principle of impulsive differential system. We impulse control the system with output feedback. And the sufficient and necessary conditions for the asymptotic stability of this system are obtained.In Chapter4, we discuss the impulsive control and synchronization of a chaotic system. We find that the different types of pulse increments will affect the stability of the impulse control system. So we consider a new chaotic system, by using Lyapunov function, obtain the sufficient condition of the impulsive con-trol and synchronization of the system with the pulse incrementBkX+Ik(X). Our results extend previous results.In Chapter5, we study a class of impulsive control of a class of Lur’e system with uncertain parameter. By using pulse control method, we obtain the criterion which guarantee the system asymptotic stability. Our results extend previous results and are more in line with the problems existing in reality.In Chapter G, we summarize the full thesis and pointed out the further re-search work.