Abstract
The synchronization problem of new discrete-time complex networks with randomly occurring coupling and distributed time-varying delay is investigated. Compared with the previous work, the distributed delay is assumed to be timevarying. Moreover, the effects of both variation range and probability distribution of distributed time-varying delay are taken into consideration. The randomly occurring coupling and distributed delay in complex networks are considered by introducing two Bernoulli stochastic variables. By using some novel analysis techniques, Kronecker product and Lyapunov functional candidate, some delay-distribution-dependent conditions are derived to ensure that the discrete-time complex network with randomly coupling and distributed time-varying delay is synchronized in mean square. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.
Highlights
Synchronization is an important property of complex networks, which can be seen in natural, social, physical and biological fields, and has been found applications in everywhere of real world 1–17
Due to the fact that time-varying delay takes the usual time delay as special case, in this paper, we aim to investigate synchronization of complex networks with the time-varying distributed delay
By employing some new techniques, the Kronecker product and linear matrix inequality LMI techniques, the synchronization criteria have been established for discrete-time complex networks with randomly distributed time-varying delay, as well as randomly occurring coupling
Summary
Synchronization is an important property of complex networks, which can be seen in natural, social, physical and biological fields, and has been found applications in everywhere of real world 1–17. In engineering applications such as network-based control, time-series analysis, and image processing, it is often necessary to formulate a discrete-time analog of the continuous-time networks. Very recently,Liu et al introduced the distributed delay in the form of constant delay into the discrete-time systems 9, 10. In practice, time-varying delay in networks occurs commonly in most designs. The study of complex networks with distributed time-varying delay is more important than those with constant delays
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