Several Stability Problems Of Fractional Impulsive Differential Systems With Delay

In describing various complicated process and phenomenon in real life, fractional impulsive differential equations are more reality than general impulsive differential equations for the global superiority of fractional derivative. Stability problems for fractional impulsive differentia system is a task with great engineering value in application. In this thesis, we mainly use Lyapunov functions, comparison principle and the representation of solutions of the investigated system to study several common stability problems for fractional impulsive differential systems with delay, we obtain several new stability criterion of the trivial solution of the studied systems.This thesis has six chapters in all:In chapter 1, the background, the present situation and the development trend of research on stability problems for fractional impulsive differential systems with delay will be introduced briefly.In chapter 2, de?nitions, properties of fractional calculus and other Lemmas,Theorems that will be used in this thesis will be sketched out.In chapter 3, the stability of a class of fractional impulsive differential uncertain control systems with delay will be taken into account. Firstly, we extent the existing Lyapunov functions and comparison principle so that they are also valid when the investigated system are de?ned by fractional derivative. Then utilizing the extended Lyapunov functions and comparison principle, we get some uniform asymptotical stability su?cient conditions for the trivial solution of the studied system.In chapter 4, we discuss the stability in terms of two measures for the fractional impulsive differential system. The main objective of this chapter is to ?nd out the stability relations of the trivial solution between the considered system and its comparison system. The ?nal result we get is: one can, under certain conditions, deduced the stability in terms of two measures of the trivial solution for the investigated system via the stability of the trivial solution for the comparison system.In chapter 5, the investigated fractional impulsive differential system with delay is de-?ned by pairwise permutable matrices. For the stability problem of this system, we can ?rstly apply the composition properties between fractional integrals and fractional derivatives to turn the investigated system into integer-order impulsive differential system with delay, then solve the integer-order impulsive system and get its representation solution, thus we obtained some exponential stability results via the representation solution for the considered system.In chapter 6, we sum up the main points of the paper and presented our main work in the future.