TY - JOUR
T1 - Finite-Time Stabilization of Markov Switching Singularly Perturbed Models
AU - Qi, Wenhai
AU - Zhang, Can
AU - Zong, Guangdeng
AU - Ahn, Choon Ki
AU - Yan, Huaicheng
N1 - Funding 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.
Publisher Copyright:
© 2004-2012 IEEE.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - 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.
AB - 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.
KW - Singularly perturbed systems
KW - asymptotic stability
KW - finite-time stability
KW - transient performance
UR - http://www.scopus.com/inward/record.url?scp=85127823969&partnerID=8YFLogxK
U2 - 10.1109/TCSII.2022.3164686
DO - 10.1109/TCSII.2022.3164686
M3 - Article
AN - SCOPUS:85127823969
VL - 69
SP - 3535
EP - 3539
JO - IEEE Transactions on Circuits and Systems I: Regular Papers
JF - IEEE Transactions on Circuits and Systems I: Regular Papers
SN - 1549-8328
IS - 8
ER -