stability analysis and feedback control of t-s fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay

in this paper, a new t-s fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. fuzzy controller is designed based on the parallel distributed compensation (pdc), and with a new lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived via linear matrix inequalities (lmis). besides, considering the differences between the model and the real system, we extent the model to uncertain t-s fuzzy hyperbolic delay model. based on the uncertain model, a robust $h_{infty}$ fuzzy controller is obtained and stability conditions are developed in terms of lmis. the main advantage of the control based on t-s fuzzy hyperbolic delay model is that it can achieve small control amplitude via ``soft'' constraint approach. finally, a numerical example and the van de vusse example are given to validate the advantages of the proposed method.