$\mathcal{H}_{\infty }$ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule

Hao Shen(沈浩)^{1,†}, Jia-Cheng Wu(吴佳成)^{1}, Jian-Wei Xia(夏建伟)^{2}, and Zhen Wang(王震)^{3}

1 College of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan 243032, China; 2 School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China; 3 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

Abstract We investigate the problem of $\mathcal{H}_{\infty}$ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule, as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously. Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an $\mathcal{H}_{\infty}$ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.

Hao Shen(沈浩), Jia-Cheng Wu(吴佳成), Jian-Wei Xia(夏建伟), and Zhen Wang(王震) $\mathcal{H}_{\infty }$ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule 2021 Chin. Phys. B 30 060203

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