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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 747890, 8 pages
http://dx.doi.org/10.1155/2013/747890
Research Article

Robust Filter Design for Itô Stochastic Pantograph Systems

1School of Electrical Engineering and Automation, Shandong Polytechnic University, Jinan 250353, China
2School of Science, Shandong Polytechnic University, Jinan 250353, China

Received 20 January 2013; Accepted 18 February 2013

Academic Editor: Weihai Zhang

Copyright © 2013 Zhiguo Yan and Yulin Huang. 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

The problem of robust filter design is investigated for stochastic pantograph systems governed by linear Itô differential equation. First, a sufficient condition for asymptotic mean-square stability of stochastic pantograph systems is presented by means of Lyapunov approach. Then, based on matrix inequalities, the filtering problem for this kind of systems is studied and a sufficient condition for the existence of the filter is derived. Furthermore, the explicit expression of the desired filter parameters is characterized. Finally, an example is given to illustrate the results.