Abstract
This paper deals with singular dynamical networks with non-delay coupling and unbounded time-delay coupling simultaneously, where the coupling configuration matrices are symmetric with zero row sums and nonnegative off-diagonal entries. A sufficient condition of synchronization is derived based on the Lyapunov-Krasovskii functional method and matrix analysis technique. A numerical example shows that our proposed method is simple and convenient in computation.
Highlights
1 Introduction In general, complex networks consist of a large number of nodes, in which every node is a fundamental cell with specific activity
Synchronization is a universal phenomenon in various fields of science and society, and many significant works have been obtained in [ – ]; Wu et al investigate synchronization of an array of linearly coupled identical systems in [ – ]; research in [, ] shows that the structure of networks must have an inevitable effect on the ability and speed of synchronization
In this paper we study synchronization problem of singular dynamical networks with non-delay coupling and unbounded timedelay coupling simultaneously
Summary
Complex networks consist of a large number of nodes, in which every node is a fundamental cell with specific activity. Koo et al [ ] and Li et al [ ] investigate synchronization of singular complex dynamical networks with time-varying bounded delays. Sufficient conditions for synchronization in terms of LMIs (linear matrix inequalities) are obtained, respectively. In this paper we study synchronization problem of singular dynamical networks with non-delay coupling and unbounded timedelay coupling simultaneously. Suppose that matrix BBis symmetric, the synchronization state s(t) of the singular delayed network ( ) is asymptotically stable if the linear time-varying singular delayed systems. Suppose that matrix BBis symmetric and Assumption holds, the singular networks with unbounded coupled delays ( ) will asymptotically synchronize in the sense of ( ). Eq ( ) is asymptotically stable about zero solution via the Lyapunov stability theory, the singular delayed network ( ) will achieve asymptotical synchronization. Comparing with [ – ], our proposed method is simple and convenient in computation
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