A New Fuzzy Guaranteed Cost Control Design for a Class of Nonlinear Discrete-Time System with Uncertainties

Abstract

This paper studies fuzzy hyperbolic guaranteed cost control for certain nonlinear systems with parameter uncertainties. As same as Takagi-Sugeno (T-S) fuzzy model, fuzzy hyperbolic model (FHM) can be used to establish the model for certain unknown complex system. Furthermore, the main advantage of using FHM over T-S fuzzy model is that no premise structure identification is need and no completeness design of premise variables space is need. Also a FHM is a kind of valid global description and nonlinear model in nature. First, the fuzzy hyperbolic model (FHM) is proposed to represent the state-space model for certain nonlinear systems. Next, a nonlinear quadratic cost function is considered as a performance measurement of the closed-loop fuzzy system. Some sufficient conditions are provided for the construction of a fuzzy hyperbolic guaranteed cost controller via state feedback. These conditions are given in terms of the feasibility of linear matrix inequalities (LMIs). A simulation example is provided to illustrate the design procedure of the proposed method.