An SOS-based Stable Control of Polynomial Discrete Fuzzy Systems

Abstract — This paper presents stability and stabilization conditions of polynomial discrete fuzzy systems. First, based on polynomial Lyapunov functions, we derive a stability condition of polynomial discrete fuzzy systems without inputs. Secondly, we derive a stabilization condition to design a stable polynomial fuzzy controller. Both of them are represented in terms of SOS and are numerically (partially symbolically) solved via the recent developed SOSTOOLS. In addition, polynomial discrete fuzzy systems and controllers contain discrete Takagi-Sugeno (T-S) fuzzy systems and controllers as a special case. Hence, the approach discussed in this paper is more general than that based on the existing LMI approaches to discrete T-S fuzzy control system designs. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our approach. I