Sampled-Data Synchronization for Complex Dynamical Networks with Time-Varying Coupling Delay and Random Coupling Strengths

Jian-An Wang,Xin-Yu Wen

doi:10.1155/2014/457457

Abstract

This paper is concerned with the problem of sampled-data synchronization for complex dynamical networks (CDNs) with time-varying coupling delay and random coupling strengths. The random coupling strengths are described by normal distribution. The sampling period considered here is assumed to be less than a given bound. By taking the characteristic of sampled-data system into account, a discontinuous Lyapunov functional is constructed, and a delay-dependent mean square synchronization criterion is derived. Based on the proposed condition, a set of desired sampled-data controllers are designed in terms of linear matrix inequalities (LMIs) that can be solved effectively by using MATLAB LMI Toolbox. Numerical examples are given to demonstrate the effectiveness of the proposed scheme.

Highlights

Many practical and natural systems can be described by models of complex networks such as internet, food webs, electric power grids, scientific citation networks, and social networks
A dynamical network can be regarded as a dynamical system with a special structure
complex dynamical networks (CDNs) are a large set of interconnected nodes, in which each node represents an element with certain dynamical system and edge represents the relationship between them

Summary

Introduction

Many practical and natural systems can be described by models of complex networks such as internet, food webs, electric power grids, scientific citation networks, and social networks. In the last few years, complex dynamical networks (CDNs) have received extensive attention and increasing interest across many fields of science and engineering [1,2,3]. It is very common that many natural systems often exhibit collective cooperative behaviors among their constituents. Synchronization, as a kind of typical collective behavior, is one of key issues in the study of complex dynamical networks. The authors in [5] focused the synchronization stability of general CDNs with coupling delay. In [6], the authors investigated the locally and globally adaptive synchronization of an uncertain complex dynamical network. The problem of globally exponential synchronization of impulsive dynamical networks was investigated in [7]. In [10], the authors studied the global exponential synchronization and synchronizability for general dynamical networks. The guaranteed cost synchronization of a CDN via dynamic feedback control was addressed in [15]

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