The Mean-Square Stability Probability of H∞ Control of Continuous Markovian Jump Systems

被引：18

作者：

Zhu, Jiaming ^{[1
]}

Yu, Xinghuo ^{[2
]}

Zhang, Tianping ^{[1
]}

Cao, Zhiqiang ^{[3
]}

Yang, Yuequan ^{[1
]}

Yi, Yang ^{[1
]}

机构：

[1] Yangzhou Univ, Dept Automat, Yangzhou, Jiangsu, Peoples R China

[2] RMIT Univ, Melbourne, Vic 3000, Australia

[3] Chinese Acad Sci, Inst Automat, Beijing, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 07期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Conditional probability; H-infinity control; Markovian jump system; mean-square stability; state observer; SLIDING-MODE CONTROL; ITO STOCHASTIC-SYSTEMS; DEPENDENT TIME-DELAYS; LINEAR-SYSTEMS; EXPONENTIAL STABILITY; DISCRETE-TIME; PARAMETERS; SUBJECT; DESIGN; FEEDBACK;

D O I：

10.1109/TAC.2015.2484357

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this technical note, H-infinity control problem of continuous Markovian jump systems is investigated. A linear feedback control scheme, combined with a state observer design, is proposed in the form of linear matrix inequalities, which can ensure the systems' mean-square stability with H-infinity performance. Then, a multistep state transition conditional probability function is introduced for the continuous Markovian process, which is used to define the system's mean-square stability probability. Furthermore, the formulas for calculating the mean-square stability probability are derived for situations where the control force may not be strong enough to ensure the full stability. Simulation results are presented to show the effectiveness of the theoretical results.

引用

页码：1918 / 1924

页数：7

共 50 条

[31] Mean-square stability of networked control systems with event driven state quantisation and packet loss
Xi, Zhiyu
IET CONTROL THEORY AND APPLICATIONS, 2018, 12 (07): : 980 - 984
[32] Robust H∞ control for Markovian jump nonlinear systems
Aliyu, M.D.S.
Boukas, E.K.
IMA Journal of Mathematical Control and Information, 2000, 17 (03) : 295 - 308
[33] H∞ Control for Ito Stochastic Systems with Markovian Jump
Gao Cun-Chen
Cong Xin-Wei
2011 30TH CHINESE CONTROL CONFERENCE (CCC), 2011, : 1338 - 1343
[34] Exponential mean-square stability of stochastic singular systems with Markov switching
Jiao, Ticao
Zheng, Wei Xing
Zong, Guangdeng
2018 37TH CHINESE CONTROL CONFERENCE (CCC), 2018, : 1570 - 1573
[35] Mean-square exponential stability of stochastic Volterra systems in infinite dimensions
Lin FU
Shiguo PENG
Feiqi DENG
Quanxin ZHU
Science China(Information Sciences), 2024, 67 (10) : 298 - 314
[36] MEAN-SQUARE STABILITY OF STOCHASTIC DIFFERENTIAL TIME-LAG SYSTEMS
LIM, CC
TEO, KL
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1989, 20 (05) : 859 - 863
[37] MEAN-SQUARE STABILITY CONDITIONS FOR DISCRETE STOCHASTIC BILINEAR-SYSTEMS
KUBRUSLY, CS
COSTA, OLV
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1985, 30 (11) : 1082 - 1087
[38] Mean-square integral input-to-state stability of nonlinear impulsive semi-Markov jump delay systems
Lin, Yu
Zhang, Yu
Bloch, Anthony
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2021, 358 (04): : 2453 - 2481
[39] EXPONENTIAL MEAN-SQUARE STABILITY OF PARTIALLY LINEAR STOCHASTIC-SYSTEMS
CHABOUR, R
FLORCHINGER, P
APPLIED MATHEMATICS LETTERS, 1993, 6 (06) : 91 - 95
[40] Mean-square exponential stability of stochastic Volterra systems in infinite dimensions
Fu, Lin
Peng, Shiguo
Deng, Feiqi
Zhu, Quanxin
SCIENCE CHINA-INFORMATION SCIENCES, 2024, 67 (10)

← 1 2 3 4 5 →