Controller Design And Stability Analysis Of Fractional-order Nonlinear System With Time-delay

Fractional calculus operators can describe complex systems better than integer calculus operators because of their memory.At the same time,time delay phenomena is very common in the actual system.However,some erratic behavior can occur to poor performances and instability,when the time delay is present in the system.Therefore the study of the stability problem for fractional-order nonlinear system with time delay has important theoretical and practical significance.In this paper,we investigate the stability and controller design problem for fractional-order nonlinear system with time delay.The main contents of this thesis are composed of the following parts:The first part studies the stability problems of fractional-order nonlinear system with time delay.Firstly,a controller is designed for the system,which cancels the nonlinear term in the system.And then two delay-independent methods for stability analysis of fractional-order linear system with time delay are proposed.The advantages and disadvantages of the two methods are analyzed by several examples.Finally,the stability region of the control parameters is obtained by the proposed method and numerical simulations are presented to verify the effectiveness of the method.In the second part,a kind of delay-dependent synchronization controller is designed for fractional order unified chaotic system with time delay.Firstly,the error system is obtained by calculating the difference between the driving system and response system in the drive-response method.And the synchronization controller is designed according to the error item and error item with time delay in error system.Secondly,the stability of the linear part of the error system with the controller is proved by Nyquist stability criterion.On the basis of the linear part stable,the stability of the whole error control system is proved by the Lyapunov function method.Finally,numerical simulations are presented to verify the effectiveness of the method,and obtain the rule about the effects of feedback coefficient on transient performance of the system.