Discrete $H_{2}/H_{\infty}$ Nonlinear Controller Design Based on Fuzzy Region Concept and Takagi–Sugeno Fuzzy Framework

The purpose of this paper is to develop a fuzzy controller to stabilize a discrete nonlinear model in which the controller rule is adjustable and it is developed for stabilizing Takagi-Sugeno (T-S) fuzzy models involving lots of plant rules. The design idea is to partition the fuzzy model into several fuzzy regions, and regard each region as a polytopic model. The proposed fuzzy controller is called the T-S fuzzy region controller (TSFRC) where the controller rule has to stabilize all plant rules of the fuzzy region and guarantee the whole fuzzy system is asymptotically stable. The stability analysis is derived from Lyapunov stability criterion in which the robust compensation is considered and is expressed in terms of linear matrix inequalities. Comparing with parallel distributed compensation (PDC) designs, TSFRC is easy to be designed and to be implemented with simple hardware or microcontroller. Even if the controller rules are reduced, TSFRC is able to provide competent performances as well as PDC-based designs