Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time

Abstract

This paper studies the problem of synchronization for a class of complex networks with discrete-time couplings. The intrinsic local dynamical behaviors of the nodes in the complex networks are varied continuously while the manners of information interaction between every two different nodes are discrete time-varying rather than proceeded continuously, that is, the communications of the nodes only active at some discrete instants. Similar to the sampled data control systems, we convert the discrete time coupling issue into an effective time-varying delayed coupling network. By constructing the Lyapunov function skillfully, sufficient conditions are derived to guarantee the realization of the synchronization pattern for all initial values based on the Lyapunov stability theorem and linear matrix inequalities. What is more, the maximum allowable sampling period for communication is obtained through a optimization problem. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.