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Technical Briefs

Stochastic Finite-Time Stabilization for Uncertain Jump Systems via State Feedback

[+] Author and Article Information
Shuping He

Institute of Automation, Jiangnan University, Wuxi, Jiangsu 214122, P. R. Chinahenyhappy@yahoo.com.cn

Fei Liu1

Institute of Automation, Jiangnan University, Wuxi, Jiangsu 214122, P. R. Chinafliu@jiangnan.edu.cn

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(3), 034504 (Apr 28, 2010) (4 pages) doi:10.1115/1.4001278 History: Received May 22, 2008; Revised February 19, 2009; Published April 28, 2010; Online April 28, 2010

The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

Copyright © 2010 by American Society of Mechanical Engineers
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