Journal of Applied Mathematics
Volume 2012 (2012), Article ID 689820, 13 pages
http://dx.doi.org/10.1155/2012/689820
Research Article

Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

Tiejun Li1,2 and Junkang Tian1,2,3

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, China
3School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 27 November 2011; Revised 26 December 2011; Accepted 27 December 2011

Academic Editor: Chong Lin

Copyright © 2012 Tiejun Li and Junkang Tian. 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 is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.