Mean square [formula omitted] synchronization for time-varying networks with double delays partial differential systems of Markov jump topology

Abstract

This paper discusses the mean-square exponential synchronization and H∞ synchronization of double time-delays partial differential systems(PDSs) with Markov jump topology. First, based on the Lyapunov functional approach and Dynkins formula, sufficient conditions are obtained for the mean-square synchronization of double time-varying delays PDSs with Markov jump topology and these conditions are presented by linear matrix inequalities (LMIs). Moreover, the mean-square H∞ synchronization of time-delay coupled PDSs with external disturbances is also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled PDSs with Markov jump topology. Finally, numerical examples of coupled time-delay PDSs are given to illustrate the correctness of the obtained results.