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

ZHANG Qianqian · KANG Yu · YU Peilong · ZHU Jin· LIU Chunhan · LI Pengfei

Journal of Systems Science & Complexity ›› 2021, Vol. 34 ›› Issue (3) : 843-859.

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Journal of Systems Science & Complexity ›› 2021, Vol. 34 ›› Issue (3) : 843-859. DOI: 10.1007/s11424-020-9263-0

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

  • ZHANG Qianqian · KANG Yu · YU Peilong · ZHU Jin· LIU Chunhan · LI Pengfei
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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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ZHANG Qianqian · KANG Yu · YU Peilong · ZHU Jin· LIU Chunhan · LI Pengfei. Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models. Journal of Systems Science and Complexity, 2021, 34(3): 843-859 https://doi.org/10.1007/s11424-020-9263-0
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