Switching clusters’ synchronization for discrete space-time complex dynamical networks via boundary feedback controls

Abstract

Unlike the existing literatures that consider only discrete-time networks, this paper explores the double effects of both discrete time and discrete spatial diffusions in a switching complex dynamical networks. By means of the knowledge of clusters controls, a clusters synchronous frame of space-time discrete switching complex networks with boundary feedback controller is newly proposed and established. With the helps of some indispensable vector-valued sequence inequalities and Lyapunov function with switching signals and clusters’ information, the boundary feedback controllers are designed to synchronize space-time discrete switching complex networks coupled with nodes’ states or spatial diffusions in the form of clusters. Additionally, a realizable computer algorithm is given to make the derived results of this paper easier to enforce. The current work is pioneering in consideration of discrete spatial diffusions and provides a theoretical and practical basis for future research in this regard.