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Technical Briefs

Finite-Time Stabilization of Stochastic Systems With Partially Known Transition Probabilities

[+] Author and Article Information
Xiao-li Luan

Key Laboratory of Advanced Control for Light Industry Processes, Ministry of Education, Institute of Automation,  Jiangnan University, Wuxi 21422, Chinaxiaoli_luan@126.com

Fei Liu1

Key Laboratory of Advanced Control for Light Industry Processes, Ministry of Education, Institute of Automation,  Jiangnan University, Wuxi 21422, Chinafliu@jiangnan.edu.cn

Peng Shi

Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd CF37 1DL, UK; School of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia; School of Mathematics and Statistics, University of South Australia, Mawson Lakes 5095, Australiapshi@glam.ac.uk

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(1), 014504 (Nov 29, 2010) (6 pages) doi:10.1115/1.4002716 History: Received March 13, 2009; Revised April 14, 2010; Published November 29, 2010; Online November 29, 2010

In this paper, the problem of finite-time stabilization for a class of uncertain Markov jump systems with partially known transition probabilities is investigated. The main aim of this paper is to derive the finite-time stabilization criteria for the underlying systems when the transition probabilities are partially known and to design a state feedback stabilizing controller such that the trajectories of the system stay within a given bound in a fixed time interval. Sufficient conditions for the existence of the desired controller are established with the linear matrix inequalities framework. A numerical example is used to illustrate the effectiveness of the developed theoretic results.

Copyright © 2011 by American Society of Mechanical Engineers
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