Stability And Synchronization Of Several Kinds Of Impulsive Systems

In recent years,the hybrid systems formed by the interaction of continuous and discrete dynamics under certain logic rules have received more and more attention,and their theoretical research results have been widely applied in various fields of science and engineering.Impulsive control is an effective method applied to hybrid systems,which can improve the transient response of the systems and realize the stability of systems.Therefore,it is great significant to discuss the stability and synchronization of impulsive control systems.On the basis of the existing research results,this paper studies the stability and synchronization of several kinds of impulsive systems.The main contents are as follows:(1)Based on the idea of switching Lyapunov function and impulsive control,the stability of proportional delay hybrid systems is studied.For proportional delay,converting proportional delay into constant delay by time transformation is adopted in the literature to obtain corresponding stability results.Without time transformation,Pachpatte’s integral inequalities are employed in this paper to establish new general criteria for exponential stability and asymptotic stability under arbitrary impulsive switching.The main conclusions are the generalization of the existing results,which can be extended to more general delay hybrid systems.(2)Based on the time-scale calculus theory,the stability of hybrid systems on time scales is studied.By means of switching impulsive control strategy,sufficient conditions for exponential stability and asymptotic stability of hybrid systems on time scales are given.The original stability criteria in continuous time domain are extended to the mixed time domain,and a unified criterion to achieve stability is given.(3)Based on the impulsive saturation structure,the impulsive control synchronization of chaotic systems described by coupled differential-difference equations is studied.Through Razumikhin theory and linear matrix inequality(LMI),some synchronization criteria for a class of timedelay coupled differential-difference chaotic systems are obtained by using the sector condition and replacing saturation nonlinearity with the dead-zone function.In the framework of saturated impulse,the existing synchronization results are extended to the coupled differential-difference equation model of the interconnection of the linear delay chaotic systems and static nonlinear operators,which provides a unified framework for many chaotic systems.