Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 750841, 16 pages
http://dx.doi.org/10.1155/2012/750841
Research Article

Robust / Filter Design for a Class of Nonlinear Stochastic Systems with State-Dependent Noise

Weihai Zhang,1 Bor-Sen Chen,2 Li Sheng,3 and Ming Gao1

1College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266590, China
2Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
3College of Information and Control Engineering, China University of Petroleum (East China), Qingdao 266555, China

Received 17 June 2012; Accepted 24 August 2012

Academic Editor: Jun Hu

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.

Abstract

This paper investigates the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise. The state and measurement are corrupted by stochastic uncertain exogenous disturbance and the dynamic system is modeled by Itô-type stochastic differential equations. For this class of nonlinear stochastic systems, the robust filter can be designed by solving linear matrix inequalities (LMIs). Moreover, a mixed / filtering problem is also solved by minimizing the total estimation error energy when the worst-case disturbance is considered in the design procedure. A numerical example is provided to illustrate the effectiveness of the proposed method.