Journal of Applied Mathematics
Volume 2012 (2012), Article ID 237430, 13 pages
http://dx.doi.org/10.1155/2012/237430
Research Article

Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

Kanit Mukdasai1,2

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand

Received 5 April 2012; Accepted 11 July 2012

Academic Editor: B. V. Rathish Kumar

Copyright © 2012 Kanit Mukdasai. 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 investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.