Chin. Phys. B, 2021, Vol. 30(6): 060203    DOI: 10.1088/1674-1056/abd7da
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# $\mathcal{H}_{\infty }$ 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.
Keywords:  Markov jump neural networks      persistent dwell-time switching rule      $\mathcal{H}_{\infty}$ state estimation      mean-square exponential stability
Received:  26 November 2020      Revised:  21 December 2020      Accepted manuscript online:  04 January 2021
 PACS: 02.30.Yy (Control theory) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61873002, 61703004, 61973199, 61573008, and 61973200).
Corresponding Authors:  Hao Shen     E-mail:  haoshen10@gmail.com

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