Design fuzzy controllers based on T-S fuzzy model via control Lyapunov function

The paper presents a novel fuzzy control design approach based on control Lyapunov function. The proposed approach can design stable controllers for a T-S fuzzy model of which the consequents are affine nonlinear state dynamic equations. The proposed fuzzy controller guarantees the stability of the closed loop system. The Sontag formula developed for affine nonlinear control systems is employed to construct a T-S fuzzy controller. Based on a control Lyapunov function approach, we derive a sufficient condition to ensure the stability of the closed loop fuzzy system. Moreover, the proposed condition leads to control Lyapunov function nonlinear standpoints that can find a desired controller directly and avoid solving simultaneous matrix inequality, which usually must be solved through numerical methods. Finally, two examples are provided to illustrate the effectiveness of our approach.