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Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models

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Abstract

This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama (EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.

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Correspondence to Yu Kang.

Additional information

This paper was supported by the National Key Research and Development Program of China under Grant Nos. 2018AAA0100800 and 2018YFE0106800, the National Natural Science Foundation of China under Grant Nos. 61725304 and 61673361, and the Science and Technology Major Project of Anhui Province under Grant No. 912198698036.

This paper was recommended for publication by Editor SUN Jian.

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Zhang, Q., Kang, Y., Yu, P. et al. Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models. J Syst Sci Complex 34, 843–859 (2021). https://doi.org/10.1007/s11424-020-9263-0

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  • DOI: https://doi.org/10.1007/s11424-020-9263-0

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