This paper deals with T–S fuzzy model with nonlinear consequent parts that has shown to reduce the number of fuzzy rules and decrease modeling error comparing with conventional T–S with linear consequent parts. To further increase the benefits of using such model, many novelties in analyzing and applying it are introduced here. Canceling the nonlinear part of subsystems by fuzzy feedback linearization, using a novel fuzzy non-quadratic Lyapunov function and new relaxation methods for further reduction of conservativeness and maximizing the region of attractions are all discussed in this paper. Numerical examples illustrate the effectiveness of the proposed method.