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Research Papers

Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition

[+] Author and Article Information
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 Wu1

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. Chinawhn@buaa.edu.cn

Yue-Sheng Luo

College of Science, Harbin Engineering University, Harbin 150001, P. R. China

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(2), 021011 (Mar 09, 2011) (7 pages) doi:10.1115/1.4003245 History: Received June 25, 2009; Revised April 06, 2010; Published March 09, 2011; Online March 09, 2011

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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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Operation mode and state trajectories of closed-loop system (Example 1)

Grahic Jump Location
Figure 2

Operation mode and state trajectories of closed-loop system (Example 2)

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