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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 869842, 11 pages
http://dx.doi.org/10.1155/2012/869842
Research Article

New Results on Stability and Stabilization of Markovian Jump Systems with Partly Known Transition Probabilities

Department of Control Science and Engineering, School of Electronics and Information Engineering, Tongji University, Shanghai 201804, China

Received 28 November 2011; Revised 21 January 2012; Accepted 28 January 2012

Academic Editor: Xue-Jun Xie

Copyright © 2012 Yafeng Guo and Fanglai Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the problem of stability and stabilization of Markovian jump linear systems with partial information on transition probability. A new stability criterion is obtained for these systems. Comparing with the existing results, the advantage of this paper is that the proposed criterion has fewer variables, however, does not increase any conservatism, which has been proved theoretically. Furthermore, a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.