A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems
Ting-Ting Gang, Jun Hu Yang, Qing Zhong Gao, Yu Zhao, Jianbin Qiu · Mathematical Problems in Engineering · 2012
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.