Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach

This paper presents guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representation of the well-known Takagi-Sugeno (T-S) fuzzy model and controller. Secondly, we derive a design condition based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this paper is more general than that based on the existing LMI approaches to T-S fuzzy control system designs. The design condition realizes guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent 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.