Stability analysis and design of type-II fuzzy controllers

This paper presents the issues of stability analysis and design of the so-called type-II fuzzy controllers, a class of fuzzy controllers whose fuzzy rules employ singleton consequents. Firstly, the analytical structure of type-II fuzzy controllers is studied in detail, and the interpolation model of double-input single-output (DISO) type-II fuzzy controllers is deduced. Secondly, a numerical methodology for the piecewise quadratic stability analysis of the closed-loop system constructed by a type-II controller and a target plant expressed by Takagi-Sugeno (T-S) fuzzy model is proposed. The new method proposed in this paper employs two new strategies to release the conservatism of the previous ones: the region-wise affine transformation and the piecewise quadratic Lyapunov function. Thirdly, the optimization and design methods of type-II fuzzy controllers are also proposed based on the interpolation model and stability analysis.