Modeling and control of T-S fuzzy hyperbolic model for a class of nonlinear systems

This paper presents a T-S fuzzy hyperbolic model for unknown nonlinear systems, by constructing a new Lyapunov function, the stability conditions of the open-loop system are given via linear matrix inequalities (LMIs). Then the parallel distributed compensation (PDC) method is used to design a fuzzy controller, and the asymptotic stability conditions of the closed-loop system are formulated by LMIs. The robust H-infinity controller is designed for an uncertain T-S fuzzy hyperbolic system with disturbances, and some sufficient conditions which ensure that the overall uncertain system is robust asymptotically stable with a prescribed H-infinity index are derived via LMIs. Finally, the validity and feasibility of the proposed schemes are demonstrated by two numerical simulation examples, moreover, some comparisons between the T-S fuzzy hyperbolic model and the T-S fuzzy linear model are given.