Research On Conrollability And Observability Of Fractional Neutral Differential Equations

The controllability and observability of the system is a very important concept in the process of studying this system.This paper studies the fractional nonlinear neutral systems with multiple delay,and gives the proof of controllability and observability under different conditions.This paper explores the situation of the multiple time-delay systems on the basis of the controllability of a single time-delay fractional order system.And we can see clearly that a single time-delay just is a special case of this article.This paper obtains the expression of the solution of the equation by using the Laplace transform,the inverse of the Laplace transform and the convolution theorem and so on.Then,the paper shows that the whole system is controllable by constructing the Gramain matrix.The structure of this paper is as follows:In chapter 1 we introduce the development background and significance of the fractional differential equations.At the same time,give some preliminary knowledge about the fractional differential equations.In chapter 2,we study the controllability problem of the fractional order system,find the solution of the system by using the Laplace transform,and construct the Gramain function to give the sufficient and necessary proof about that the system is controllable.At the same time,it gives the proof about the observability of systems.In chapter 3,we study the controllability and observability of the neutral differential systems when the order is between 1 and 2.In chapter 4,we give the existence of solutions for fractional order impulsive systems,and prove that the system is controllable.