Modeling and control of Takagi-Sugeno fuzzy hyperbolic model for a class of nonlinear systems

In this paper, a Takagi-Sugeno (T-S) fuzzy hyperbolic model is proposed for the fuzzy control of a class of nonlinear systems. The consequence of the proposed model is a hyperbolic tangent dynamic model, and it is employed to represent the nonlinear system. By constructing a new Lyapunov function, the stability conditions of the open-loop T-S fuzzy hyperbolic system are derived via linear matrix inequalities (LMIs). Then, the parallel distributed compensation (PDC) method is used to design a fuzzy hyperbolic controller, and the asymptotic stability conditions of the closed-loop system are formulated via LMIs. The main advantage of the control based on T-S fuzzy hyperbolic model is that it can achieve small control amplitude via "soft" constraint control approach. Finally, the effectiveness and advantage of the proposed schemes are illustrated by a mathematical constructive example and the Van de Vusse example.