Intermittent control to stationary distribution and exponential stability for hybrid multi-stochastic-weight coupled networks based on aperiodicity |
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| Authors: | Yan Liu Henglei Xu Wenxue Li |
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| Institution: | Department of Mathematics, Harbin Institute of Technology, Weihai 264209, PR China |
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| Abstract: | In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes. |
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| Keywords: | Corresponding author |
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