Adaptive synchronization of uncertain stochastic impulsive systems with varying time-delays

In this paper, an adaptive controller is designed for synchronizing a class of uncertain delayed master-slave impulsive stochastic systems. The unmodeled dynamics is assumed to be bounded and the adaptive control contains the time-varying coefficient matrix. Based on Lyapunov-Krasovskii functional and free-weighting matrix method, the synchronization of stochastic systems is achieved in the mean square sense through appropriate proposed adaptive controller. To solve derived conditions that are expressed in terms of LMIs, LMI (Linear Matrix Inequality) Toolbox in Matlab can be utilized. Finally, synchronization of Lorenz system is employed to exemplify the effectiveness and applicability of the proposed result in the numerical section.