On local non-quadratic guaranteed cost control for continuous-time Takagi-Sugeno models

This paper focuses on the problem of guaranteed cost control for continuous-time nonlinear models in the Takagi-Sugeno (T-S) form. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. New guaranteed cost control strategy is derived based on the non-quadratic Lyapunov function and non-PDC control law. The well known problem of handing time-derivatives of membership function (MFs) is overcomed by reducing global goals to the estimation of region of attraction. It is shown that the derived local conditions actually lead to reasonable advantages over the existing quadratic approach. Moreover, conditions for the solvability of the guaranteed cost controller design given here are written in the form of linear matrix inequalities (LMIs) which can be efficiently solved by convex optimization techniques. Simulation example is given to demonstrate the validity of the proposed approaches.