TY - JOUR
T1 - Mean‐square strong stability and stabilization of discrete‐time stochastic systems with multiplicative noises
AU - Yan, Zhiguo
AU - Su, Fangxu
AU - Gao, Zhiwei
N1 - Funding information: This work was supported by the National Natural Science Foundation of China (No. 61877062, 61977043).
PY - 2022/8/1
Y1 - 2022/8/1
N2 - This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. First, the definition of the mean-square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS-strong stability are derived. Moreover, the relationship between MS-strong stability and MS-stability is given. Second, some necessary and sufficient conditions of the MS-strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.
AB - This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. First, the definition of the mean-square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS-strong stability are derived. Moreover, the relationship between MS-strong stability and MS-stability is given. Second, some necessary and sufficient conditions of the MS-strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.
KW - discrete-time stochastic system
KW - mean-square stability
KW - mean-square strong stability
KW - outputfeedback
KW - overshoot
UR - http://www.scopus.com/inward/record.url?scp=85128818004&partnerID=8YFLogxK
U2 - 10.1002/rnc.6161
DO - 10.1002/rnc.6161
M3 - Article
VL - 32
SP - 6767
EP - 6784
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
SN - 1049-8923
IS - 12
ER -