Abstract and Applied Analysis
Volume 2012 (2012), Article ID 450168, 22 pages
http://dx.doi.org/10.1155/2012/450168
Research Article

Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

Lianglin Xiong,1 Xiaobing Zhou,2 Jie Qiu,3 and Jing Lei1

1School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, China
2School of Information Science and Engineering, Yunnan University, Kunming 650091, China
3Library of Yunnan, University of Nationalities, Kunming 650031, China

Received 6 May 2012; Accepted 19 September 2012

Academic Editor: Ziemowit Popowicz

Copyright © 2012 Lianglin Xiong et al. 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

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.