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ℋ ∞ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching ruleProject supported by the National Natural Science Foundation of China (Grant Nos. 61873002, 61703004, 61973199, 61573008, and 61973200).
Chinese Physics B ( IF 1.7 ) Pub Date : 2021-06-03 , DOI: 10.1088/1674-1056/abd7da
Hao Shen 1 , Jia-Cheng Wu 1 , Jian-Wei Xia 2 , Zhen Wang 3
Affiliation  

We investigate the problem of 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 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.



中文翻译:

ℋ ∞ 具有转移概率的马尔可夫跳跃神经网络状态估计受持续驻留时间切换规则国家自然科学基金资助项目(批准号 61873002、61703004、61973199、61573008 和 61973200)。

我们研究ℋ∞的 问题离散时间马尔可夫跳跃神经网络的状态估计。假设马尔可夫链的转移概率是分段时变的,采用持续驻留时间切换规则作为更通用的切换规则来描述这种变化特征。然后,基于经典的李雅普诺夫稳定性理论,建立了一个李雅普诺夫函数,其中同时考虑了系统模态的马尔可夫跳跃特征和转移概率的持续驻留时间切换信息。此外,通过使用随机分析方法和一些先进的矩阵变换技术,得到了一些充分条件,使得估计误差系统是均方指数稳定的ℋ∞ 性能水平,从中可以得到估算器的具体形式。最后通过数值算例验证了所得结果的合理性和有效性。

更新日期:2021-06-03
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