This paper is concerned with nonquadratic conditions for stabilization of continuous-time nonlinear systems via exact Takagi-Sugeno models and generalized fuzzy Lyapunov functions. The approach hereby proposed feedback to the time derivatives of the membership functions through a multi-index control law that cancels out the terms responsible of former a priori local conditions. Thus, a nonquadratic controller design in the form of linear matrix inequalities is achieved; it does not require bounds on the time derivatives nor any extra parameters. The examples included are shown to outperform former approaches.