Abstract and Applied Analysis
Volume 2012 (2012), Article ID 348418, 20 pages
http://dx.doi.org/10.1155/2012/348418
Research Article

Robust Exponential Stability Criteria of LPD Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

Kanit Mukdasai,1,2 Akkharaphong Wongphat,1 and Piyapong Niamsup2,3

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 15 October 2012; Accepted 15 November 2012

Academic Editor: Elena Braverman

Copyright © 2012 Kanit Mukdasai 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 investigates the problem of robust exponential stability for linear parameter-dependent (LPD) systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.