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

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 sys...

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Bibliographic Details
Published in:Journal of systems science and complexity 2021-06, Vol.34 (3), p.843-859
Main Authors: Zhang, Qianqian, Kang, Yu, Yu, Peilong, Zhu, Jin, Liu, Chunhan, Li, Pengfei
Format: Article
Language:English
Subjects:
Clustering
Complex Systems
Control
Control systems design
Discrete time systems
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Stabilization
Statistics
Switching
Systems Theory
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Summary: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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-020-9263-0