Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

Abstract

AbstractThis paper studies the problem of non‐fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time‐varying coupling delays. By constructing a new Lyapunov–Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability‐distribution‐dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non‐fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.