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Journal of Applied Mathematics
Volume 2013, Article ID 269091, 13 pages
http://dx.doi.org/10.1155/2013/269091
Research Article

Delay-Dependent Finite-Time Filtering for Markovian Jump Systems with Different System Modes

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
3Key Laboratory on Signal and Information Processing, Xihua University, Chengdu, Sichuan 610039, China

Received 4 March 2013; Accepted 16 April 2013

Academic Editor: Qiankun Song

Copyright © 2013 Yong Zeng 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

This paper is concerned with the problem of delay-dependent finite-time filtering for Markovian jump systems with different system modes. By using the new augmented multiple mode-dependent Lyapunov-Krasovskii functional and employing the proposed integrals inequalities in the derivation of our results, a novel sufficient condition for finite-time boundness with an performance index is derived. Particularly, two different Markov processes have been considered for modeling the randomness of system matrix and the state delay. Based on the derived condition, the filtering problem is solved, and an explicit expression of the desired filter is also given; the system trajectory stays within a prescribed bound during a specified time interval. Finally, a numerical example is given to illustrate the effectiveness and the potential of the proposed techniques.