Delayed nonquadratic L 2 -stabilization of continuous-time nonlinear Takagi–Sugeno fuzzy models

This work deals with the design of fuzzy controllers for stabilization of continuous-time nonlinear systems subject to disturbances, which are represented by nonlinear Takagi–Sugeno fuzzy models, i.e., Takagi–Sugeno fuzzy models with nonlinear consequents. A nonquadratic Lyapunov function is used to derive sufficient design conditions based on linear matrix inequality constraints as well as to reduce the conservativeness when compared to existing control approaches in the literature. Furthermore, the nonquadratic Lyapunov function is defined in terms of an integral membership function, which leads to a delayed nonquadratic -stabilization condition. This condition avoids the well-known difficulties in dealing with time derivatives of membership functions and/or path-independent conditions, found in most of the nonquadratic control approaches for continuous-time Takagi–Sugeno fuzzy models. Two numerical examples are performed to illustrate the reduction in conservativeness provided by the proposed approach.