Study On Impulsive Control And Synchronization Of The Memristive-chaotic System

As a high efficiency, low cost control form, impulsive control provides an effective method for the control of chaotic systems. However, the existing results are mostly for the systems fixed times impulse, and in the actual operation process, it is difficult to determine the exact time of the impulse. In order to solve this problem, researchers may think if the impulse time occurs randomly in a time zone, which called impulse time window, this will solve the problem which is difficult to determine at a fixed time. In practical operation of the memristor chaotic system, the parameter errors are inevitable;the parameter errors to some extent will affect the synchronization quality of the chaotic systems. That is, two coupling systems cannot achieve complete synchronization, but we need to find a small positive parameter ? which makes the error between the two systems does not exceed the norm of ?, so that the two systems achieve quasi synchronization with the ? boundary error. The main contents of this paper are as follows:Firstly, the memristor chaotic system with impulse window is established. Applying impulse control on the system, by using the Lyapunov function method and comparison principle, the sufficient condition of asymptotically stable of the memristor chaotic circuit system is obtained. Secondly, since the parameter has certain errors in the actual process of synchronization of chaotic systems operation, the synchronization quality deteriorates. Therefore, this paper estimates the synchronization error bounds, as far as possible, reduce the error converge to a small area; get a sufficient condition of the proposed synchronization of memristor chaotic systems when the parameter error exist. Finally,since the synchronization type is not the same, use Lyapunov stability theory, an effective controller is designed,and then realizes synchronization of two chaotic system.