### 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

1. ZHANG Qianqian
Department of Automation, University of Science and Technology of China, Hefei 230026, China.Email: ZQQ789@mail.ustc.edu.cn.
KANG Yu (Corresponding author)
Department of Automation, University of Science and Technology of China, Hefei 230026, China; Institute of Advanced Technology, University of Science and Technology of China, Hefei 230026, China.
Email: kangduyu@ustc.edu.cn.
YU Peilong · ZHU Jin · LIU Chunhan · LI Pengfei
Department of Automation, University of Science and Technology of China, Hefei 230026, China.
Email: ypl8432@mail.ustc.edu.cn; jinzhu@ustc.edu.cn; lch666@mail.ustc.edu.cn; puffylee@mail.ustc.edu.cn.
• Online:2021-06-25 Published:2021-03-11

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[J]. Journal of Systems Science and Complexity, 2021, 34(3): 843-859.

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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