Stability Analysis Of Delay Differential System And Its Existence And Uniqueness Of The Solution

This paper disscussed the stability of the delay differential systems and descriptor systems with time-varying delay. The existence and uniqueness theorems of the fractional order differential systems have been presented,and some conclusions are drawn. The full text is divided into five chapters.The first chapter mainly introduces the delay differential system,fractional calculus and fractional differential systems.We present some background and prepare knowledge,the structure and arrangement of this paper.The second chapter discusses continuous system with two different time-varying de-lays and its stability criterion.The criterion is proposed by using appropriate Lyapunov-Krasovskii function method and a new estimation method,This method did not take the way of model transformation and liberty matrix, compared with the existing results,the new method greatly reduced matrix variables, calculation complexity and less conserva-tive,Criterion consists of a set of linear matrix inequality (LMI), criterion can use LMI toolbox in Matlab software to test and verify.Finally, numerical examples verify the effec-tiveness of the method and advantage.The third chapter presents a new result of stability analysis for uncertain descrip-tor systems with time-varying delay,new delay-dependent robust stability criterion of uncertain time-delay descriptor systems is proposed by exploiting appropriate Lyapunov-Krasovskii functional candidate.This criterion is expressed by a set of linear matrix in-equalities,which can be tested by using the LMI toolbox in Matlab.Finally,illustrative examples demonstrate the effectiveness and the advantage of the proposed method.In the forth chapter,based on the Lyapunov stability theory and in the view of the fractional order delay system, put forward a kind of determination methods stability, and given the mathematical proof.The theorem used in fractional order delay chaos system synchronization,Realize the unknown parameters fractional order delay of adaptive back-stepping chaotic system, and the example results verify that the theory was formed.Finally, we presented the existence and uniqueness theorems for the initial value problem of neutral fractional systems with time-delay. Moreover,sufficient conditions for the finite time stability for the system are obtained.