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Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching. (English) Zbl 1301.93152

Summary: In this paper, the issue of exponential synchronization for a class of stochastic coupled networks with Markovian switching is investigated. Based on some results in graph theory, Lyapunov stability theory and state feedback control technique, several sufficient criteria have been derived to ensure the \(p \operatorname{th}\) moment exponential stability and almost sure exponential stability for the error network. This means that – under these sufficient criteria – drive-response coupled networks can be \(p \operatorname{th}\) moment exponentially synchronized and almost surely exponentially synchronized, respectively. Finally, stochastic Cohen-Grossberg neural networks with Markovian switching is employed to illustrate our feasible results.

MSC:

93E03 Stochastic systems in control theory (general)
90B15 Stochastic network models in operations research
94C15 Applications of graph theory to circuits and networks
93D20 Asymptotic stability in control theory
93E15 Stochastic stability in control theory
93B20 Minimal systems representations
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