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Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

Yuqian Lin, Guangming Zhuang*, Jianwei Xia, Wei Sun, and Junsheng Zhao
International Journal of Control, Automation, and Systems, vol. 20, no. 3, pp.909-923, 2022

Abstract : In this paper, the problem of asynchronous robust H∞ dynamic output feedback control for Markovian jump neural networks with norm-bounded parameter uncertainties and mode-dependent time-varying delays is investigated. The improved delay-dependent stochastic stability conditions and bounded real lemma are obtained by introducing the relaxation variables, which reduces the conservatism caused by boundary technology and model transformation. An improved Lyapunov-Krasovskii functional is constructed using linear matrix inequalities. On this basis, the solution of robust H∞ dynamic output feedback problem and sufficient conditions for solving the problem of asynchronous dynamic output feedback controller are given respectively. Asynchronous dynamic output feedback controller is constructed to ensure that the closed-loop mode-dependent time-varying delays Markovian jump neural networks achieve different convergence speeds. The given H∞ performance index is satisfied for the delays not bigger than a given upper bound. Numerical examples are employed to show the effectiveness and correctness of the method presented in this paper.

Keyword : Dynamic output feedback control, linear matrix inequality, Markovian jump system, time-varying delay, neural networks.

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