Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 439805, 17 pages
http://dx.doi.org/10.1155/2012/439805
Research Article

A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

Ting-Ting Gang,1 Jun Yang,1 Qing Gao,2,3 Yu Zhao,1 and Jianbin Qiu4

1School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
2Department of Automation, University of Science and Technology of China, Hefei 230027, China
3Department of Mechanical and Biomedical Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
4Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China

Received 28 November 2012; Accepted 14 December 2012

Academic Editor: Peng Shi

Copyright © 2012 Ting-Ting Gang 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 stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.