This brief is concerned with the issue of finite-time stabilization of discrete-time stochastic singularly perturbed models, in which the stochastic process is regulated by a Markov chain with partially unknown transition probabilities (TPs). The slow-state and fast-state variable are considered in the modeling, and the corresponding Markov switching model with a singularly perturbed parameter is obtained in a unified framework. Ill-conditioned problems caused by a small singular perturbation parameter are prevented by developing a finite-time stability criterion for the resultant system. Furthermore, feasible conditions are derived for the desired finite-time state feedback controller by using matrix inequalities that are independent of the singularly perturbed parameter. Finally, a gear-driven DC motor model is applied to illustrate the effectiveness of the described control strategy.
|Number of pages
|IEEE Transactions on Circuits and Systems II: Express Briefs
|Published - 2022 Aug 1
Bibliographical noteFunding Information:
This work was supported in part by the Natural Science Foundation of Shandong under Grant ZR2019YQ29 and Grant ZR2021MF083; in part by the National Natural Science Foundation of China under Grant 62073188 and Grant 61773235; and in part by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (Ministry of Science and ICT) under Grant NRF-2020R1A2C1005449.
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- Singularly perturbed systems
- asymptotic stability
- finite-time stability
- transient performance
ASJC Scopus subject areas
- Electrical and Electronic Engineering