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Exponential Stabilization of Delayed Complex-valued Neural Networks with Aperiodic Sampling: A Free-matrix-based Time-dependent Lyapunov Functional Method

Lan Yao, Zhen Wang*, Qingbiao Wang, Jianwei Xia, and Hao Shen
International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp.1894-1903, 2020

Abstract : In this paper, the exponential stabilization of delayed complex-valued neural networks (DCNNs) is addressed via sampled-data control. First, aperiodic sampled-data control aimed at further reducing the frequency of data transmission is adopted, which covers the periodic sampling as a special case. Then, a free-matrix-based timedependent Lyapunov functional is specially constructed for stability analysis of closed-loop DCNNs, in which two extra free matrices are introduced and the available information of system states at the sampling instants are fully utilized. Accordingly, some less conservative stability conditions are established. By resorting to a matrix transformation, the design scheme for the feedback gains can be obtained. Meanwhile, the qualitative relationship between the decay rate and the upper bound of the variable sampling period is established and the maximum allowable value of the variable sampling period is determined. Finally, an illustrative example is provided to demonstrate the feasibility of the proposed stabilization criteria.

Keyword : Aperiodic sampled-data control, delayed complex-valued neural networks, exponential stabilization, free-matrix-based Lyapunov functional

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