Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 834643, 15 pages
http://dx.doi.org/10.1155/2012/834643
Research Article

Stability and Stabilization of Networked Control System with Forward and Backward Random Time Delays

Ye-Guo Sun1 and Qing-Zheng Gao2

1Department of Mathematics and Computational Science, Huainan Normal University, Huainan 232038, China
2Department of Physics and Information Engineering, Jining University, Qufu 273155, China

Received 14 August 2011; Revised 20 October 2011; Accepted 24 October 2011

Academic Editor: Xue-Jun Xie

Copyright © 2012 Ye-Guo Sun and Qing-Zheng Gao. 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 deals with the problem of stabilization for a class of networked control systems (NCSs) with random time delay via the state feedback control. Both sensor-to-controller and controller-to-actuator delays are modeled as Markov processes, and the resulting closed-loop system is modeled as a Markovian jump linear system (MJLS). Based on Lyapunov stability theorem combined with Razumikhin-based technique, a new delay-dependent stochastic stability criterion in terms of bilinear matrix inequalities (BMIs) for the system is derived. A state feedback controller that makes the closed-loop system stochastically stable is designed, which can be solved by the proposed algorithm. Simulations are included to demonstrate the theoretical result.