This paper studies the problem of robustly stochastic stability and stabilization for a class of uncertain Markov jump linear systems with time delay. A new stochastic Lyapunov–Krasovskii functional (LKF) is constructed for the stability analysis and stabilization, in which the delay is uniformly divided into multiple segments. Based on this LKF and using an improved Jensen's integral inequality, the improved delay-dependent stochastic stability criteria are first derived in terms of linear matrix inequalities (LMIs). Then, an LMI approach to the design of stabilizing controllers via delayed state feedback is developed. The previous stability criteria are extended to give the delay-dependent stabilization conditions in terms of LMIs. Furthermore, an LMI optimization algorithm is proposed to find the maximum allowable delay of the system. Finally, numerical examples show that the proposed results are effective and much less conservative than some existing results.
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e-mail: whn@buaa.edu.cn
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March 2011
Research Papers
Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition
Jun-Wei Wang,
Jun-Wei Wang
National Key Laboratory of Science and Technology on Holistic Control, School of Automation Science and Electrical Engineering,
Beihang University (Beijing University of Aeronautics and Astronautics)
, Beijing 100191, P. R. China
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Huai-Ning Wu,
Huai-Ning Wu
National Key Laboratory of Science and Technology on Holistic Control, School of Automation Science and Electrical Engineering,
e-mail: whn@buaa.edu.cn
Beihang University (Beijing University of Aeronautics and Astronautics)
, Beijing 100191, P. R. China
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Yue-Sheng Luo
Yue-Sheng Luo
College of Science,
Harbin Engineering University
, Harbin 150001, P. R. China
Search for other works by this author on:
Jun-Wei Wang
National Key Laboratory of Science and Technology on Holistic Control, School of Automation Science and Electrical Engineering,
Beihang University (Beijing University of Aeronautics and Astronautics)
, Beijing 100191, P. R. China
Huai-Ning Wu
National Key Laboratory of Science and Technology on Holistic Control, School of Automation Science and Electrical Engineering,
Beihang University (Beijing University of Aeronautics and Astronautics)
, Beijing 100191, P. R. Chinae-mail: whn@buaa.edu.cn
Yue-Sheng Luo
College of Science,
Harbin Engineering University
, Harbin 150001, P. R. ChinaJ. Dyn. Sys., Meas., Control. Mar 2011, 133(2): 021011 (7 pages)
Published Online: March 9, 2011
Article history
Received:
June 25, 2009
Revised:
April 6, 2010
Online:
March 9, 2011
Published:
March 9, 2011
Citation
Wang, J., Wu, H., and Luo, Y. (March 9, 2011). "Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition." ASME. J. Dyn. Sys., Meas., Control. March 2011; 133(2): 021011. https://doi.org/10.1115/1.4003245
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