The Study Of The Synchronization And Control Of Chaotic System

The phenomenon of chaos is a kind of quasi-stochastic dynamical behaviors ofdeterminate nonlinear systems, and the nature of chaos is the extreme sensitivity to changein initial conditions. Since chaos has been proposed, it has attracted common attention andhas been extensively studied, and some fruitful research results have been achieved. Withthe constant understanding of chaos, people begin to use and control chaos. However, dueto the complexity and the sensitivity to the initial conditions of chaotic systems themselves,the research on the chaos control is becoming more and more challenging and significant.In this thesis, based on the state feedback control, observer control and fuzzy control,the problems of the control and the synchronization of chaotic system are studied byconstructing appropriate Lyapunov-Krasovskii functional. The main works are as follows:First of all, for uncertain identical time-delay chaotic systems, the problem of thesynchronization is studied by state feedback control and linear matrix inequality methods.Secondly, thanks to many uncertain factors, the synchronization problem of twoidentical chaotic systems with unmatched disturbance is proposed and the sufficientconditions are obtained.Thirdly, by constructing appropriate Lyapunov-Krasovskii functional and state observer,the problem of the chaos control based on the observer is studied, and the synchronizationbetween the state system and the observer system is achieved by linear matrix inequalitymethods.Finally, the problem of time-delay chaotic system based on fuzzy model is proposed byconstructing appropriate Lyapunov-Krasovskii functional and PDC technique, and thesufficient conditions are given which satisfy the H￥synchronization.