Global cluster synchronization in finite time for complex dynamical networks with hybrid couplings via aperiodically intermittent control
Qijng Yang, Huaiqin Wu, Jinde Cao
Abstract
Summary In this article, we investigate the cluster synchronization in finite time for nonlinear complex dynamical networks (CDNs) with hybrid couplings via aperiodically intermittent control. First, a new lemma with respect to the convergence in finite time is developed for the nonnegative continuous functions. Second, the classification controller, which is dependent of the coupling of the dynamic nodes among different clusters, is designed to realize the cluster synchronization goal. Third, by means of the Lyapunov functional approach, the inequality analysis technique, and the proposed lemmas, the global cluster synchronization conditions in finite time are addressed in terms of linear matrix inequalities (LMIs) for CDNs via discontinuous feedback control scheme with integral terms. Moreover, the global cluster synchronization conditions in finite time is also achieved in the form of LMIs for CDNs with hybrid couplings via aperiodically intermittent control. In addition, the settling time, which is closely related to the topological structure of networks and the maximum ratio of the rest width to the aperiodic time span, is estimated accurately. Finally, the effectiveness of theoretical results is verified by two simulation examples.