Stabilization of Polynomial Fuzzy Systems via a Sum of Squares Approach

This paper presents stabilization of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we propose a polynomial fuzzy controller that is a more general representation of the well-known Takagi-Sugeno (T-S) fuzzy controller. Secondly, we derive stabilization conditions based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, stabilization approach discussed in this paper is more general than that based on the existing LMI approaches to T-S fuzzy control system designs. The stabilization conditions in the proposed approach can be represented in terms of SOS and are numerically (partially symbolically) solved via the developed SOSTOOLS. To illustrate the validity of the design approach, a design example is provided. The example shows that our approach provides more relaxed design results than the existing LMI approach.