TY - JOUR
T1 - Finite-Time Annular Domain Stability and Stabilization of Stochastic Systems With Semi-Markovian Switching
AU - Yan, Zhiguo
AU - Zhou, Xiaomin
AU - Chang, Gaizhen
AU - Gao, Zhiwei
N1 - Funding information: This work is supported by the National Natural Science Foundation of China under Grant Nos. 61877062, 61977043, and the Cultivating Foundation of Qilu University of Technology Grant Nos. 2022PYI010.
PY - 2022/12/12
Y1 - 2022/12/12
N2 - In this paper, finite-time annular domain stability and stabilization of Itô stochastic systems with semi-Markovian switching are investigated, where the switching frequency is timevarying, and satisfies a unfixed polytope. A new inequality called reverse differential Gronwall inequality is proposed to address less conservative sufficient conditions for testing the finitetime annular domain stability, and its superiority to modified Gronwall inequality is analyzed. Moreover, sufficient conditions for the existence of state feedback and observer-based finitetime annular domain stabilizing controllers are obtained. In the sequel, a L × N -mode algorithm is presented for bridging the relationship between the adjustable parameters and the range of transition rates. Finally, an example is provided to illustrate the effectiveness of the proposed methods.
AB - In this paper, finite-time annular domain stability and stabilization of Itô stochastic systems with semi-Markovian switching are investigated, where the switching frequency is timevarying, and satisfies a unfixed polytope. A new inequality called reverse differential Gronwall inequality is proposed to address less conservative sufficient conditions for testing the finitetime annular domain stability, and its superiority to modified Gronwall inequality is analyzed. Moreover, sufficient conditions for the existence of state feedback and observer-based finitetime annular domain stabilizing controllers are obtained. In the sequel, a L × N -mode algorithm is presented for bridging the relationship between the adjustable parameters and the range of transition rates. Finally, an example is provided to illustrate the effectiveness of the proposed methods.
KW - Finite-time annular domain stability
KW - Stochastic systems
KW - Semi-Markovian switching
KW - Gronwall inequality
U2 - 10.1109/tac.2022.3228202
DO - 10.1109/tac.2022.3228202
M3 - Article
SP - 1
EP - 8
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
ER -