Journal of Applied Mathematics
Volume 2013 (2013), Article ID 368259, 10 pages
http://dx.doi.org/10.1155/2013/368259
Research Article

New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

P. Niamsup1,2 and G. Rajchakit3

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiangmai 50200, Thailand
2Center of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Division of Mathematics and Statistics, Faculty of Science, Maejo University, Chiangmai 50290, Thailand

Received 17 January 2013; Revised 1 April 2013; Accepted 15 April 2013

Academic Editor: Rung Ching Chen

Copyright © 2013 P. Niamsup and G. Rajchakit. 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 addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.