Exponential synchronization of stochastic impulsive perturbed chaotic Lur''e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponentialsynchronization for uncertain stochastic impulsive perturbed chaoticLur'e systems. The parametric uncertainty is assumed to be normbounded. Based on the Lyapunov function method, time-varying delayfeedback control technique and a modified Halanay inequality forstochastic differential equations, several sufficient conditions arepresented to guarantee the exponential synchronization in meansquare between two identical uncertain chaotic Lur'e systems withstochastic and impulsive perturbations. These conditions areexpressed in terms of linear matrix inequalities (LMIs), which caneasily be checked by utilizing the numerically efficient Matlab LMItoolbox. It is worth pointing out that the approach developed inthis paper can provide a more general framework for thesynchronization of multi--perturbation chaotic Lur'e systems, whichreflects a more realistic dynamics. Finally, a numerical example isprovided to demonstrate the effectiveness of the proposed method.