Pinning sampled-data control for synchronization of complex networks with probabilistic time-varying delays using quadratic convex approach

Abstract

This paper addresses pinning sampled-data synchronization problem for complex dynamical networks with probabilistic time-varying coupling delays and control packet loss. The sampling period considered here is assumed to be less than a given bound. By introducing a Bernoulli distributed stochastic variable, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. A new Lyapunov–Krasovskii functional (LKF) is constructed and by using quadratic convex approach, reciprocal convex technique and Jensen׳s inequality, sufficient conditions for the synchronization of complex networks are derived. Based on the average dwell-time method and delay-probability-distribution-dependent condition, the synchronization criterion is derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed techniques.