H∞-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays

Abstract

This paper investigates the synchronization of complex dynamical networks with coupling delays and external disturbances by applying local feedback injections to a small fraction of nodes in the whole network. Based on $H_{\infty }$ control theory, some delay-independent and -dependent synchronization criteria with a prescribed $H_{\infty }$ disturbances attenuation index are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to reach network synchronization. A simulation example is included to validate the theoretical results.