Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 760878, 20 pages
http://dx.doi.org/10.1155/2011/760878
Research Article

Delay-Dependent 𝐻 ∞ Filtering for Singular Time-Delay Systems

Zhenbo Li1,2 and Shuqian Zhu3

1School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, China
2Shandong Provincial Key Laboratory of Digital Media Technology, Shandong Economic University, Jinan 250014, China
3School of Mathematics, Shandong University, Jinan 250100, China

Received 14 February 2011; Accepted 29 April 2011

Academic Editor: Xue He

Copyright © 2011 Zhenbo Li and Shuqian Zhu. 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 deals with the problem of delay-dependent 𝐻 ∞ filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribed 𝐻 ∞ performance 𝛾 is given in terms of linear matrix inequalities (LMIs). Then, the sufficient condition is obtained for the existence of the 𝐻 ∞ filter, and the explicit expression for the desired 𝐻 ∞ filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.