Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays

Abstract

This paper is concerned with the cluster synchronization in finite time for a class of complex networks with nonlinear coupling strengths and probabilistic coupling delays. The complex networks consist of several clusters of nonidentical discontinuous systems suffered from uncertain bounded external disturbance. Based on the Takagi–Sugeno (T–S) fuzzy interpolation approach, we first obtain a set of T–S fuzzy complex networks with constant coupling strengths. By developing some novel Lyapunov functionals and using the concept of Filippov solution, some new analytical techniques are established to derive sufficient conditions ensuring the cluster synchronization in a setting time. In particular, this paper extends the pinning control strategies for networks with continuous-time dynamics to discontinuous networks. Numerical simulations demonstrate that the theoretical results are effective and the T–S fuzzy approach is important for relaxed results.