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Journal of Applied Mathematics
Volume 2013, Article ID 545636, 16 pages
http://dx.doi.org/10.1155/2013/545636
Research Article

Delay-Dependent Control for Descriptor Markovian Jump Systems with Time-Varying Delay

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2School of Science, Shenyang University of Technology, Shenyang 110870, China

Received 11 August 2013; Accepted 20 September 2013

Academic Editor: Baolin Wang

Copyright © 2013 Jinghao Li 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 delay-dependent control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribed performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.