Synchronization of a Class of Discrete-Time Nonlinear Singularly Perturbed Complex Networks†

Abstract

In this paper, the problem of synchronization is investigated for a class of discrete-time nonlinear singularly perturbed complex networks (SPCNs). A slow sampling discrete-time nonlinear SPCN model is first devised, which includes the slow and the fast states as well as the general sector-like nonlinear functions. By utilizing the Kronecker product, a new Lyapunov function dependent on singular perturbation parameter (SPP) is constructed. A sufficient condition in terms of linear matrix inequalities (LMIs) is derived under which the discrete-time nonlinear SPCN is globally asymptotically synchronized. When these LMIs have feasible solutions, the global asymptotic synchronization is ensured and the upper bound of the SPP is evaluated. A numerical example is given to illustrate the effectiveness of our results.