Abstract and Applied Analysis
Volume 2011 (2011), Article ID 860506, 15 pages
http://dx.doi.org/10.1155/2011/860506
Research Article
An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales
1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
3Center of Excellence in Mathematics CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
4Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiangmai 50200, Thailand
Received 17 December 2010; Revised 3 May 2011; Accepted 19 May 2011
Academic Editor: Martin D. Schechter
Copyright © 2011 Kanit Mukdasai and Piyapong Niamsup. 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
We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.