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Mathematical Problems in Engineering
Volume 2012, Article ID 231352, 15 pages
Research Article

Robust Filtering for General Nonlinear Stochastic State-Delayed Systems

1College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China
2Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
3School of Electronic Information and Control Engineering, Shandong Polytechnic University, Jinan 250353, China

Received 3 July 2011; Accepted 24 August 2011

Academic Editor: Xue-Jun Xie

Copyright © 2012 Weihai Zhang 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.


This paper studies the robust H filtering problem of nonlinear stochastic systems with time delay appearing in state equation, measurement, and controlled output, where the state is governed by a stochastic Itô-type equation. Based on a nonlinear stochastic bounded real lemma and an exponential estimate formula, an exponential (asymptotic) mean square H filtering design of nonlinear stochastic time-delay systems is presented via solving a Hamilton-Jacobi inequality. As one corollary, for linear stochastic time-delay systems, a Luenberger-type filter is obtained by solving a linear matrix inequality. Two simulation examples are finally given to show the effectiveness of our results.