An Improved Fault-Tolerant Control and Stabilization for Positive Polynomial Fuzzy Systems

This paper presents an improved analysis method to design a fault-tolerant controller for positive polynomial fuzzy systems based on static output feedback as well as actuator faults. Firstly, inspired by the property of fault matrix, a new approach of controller design is presented, and some constraint conditions are introduced to guarantee the stability conditions and posi-tivity conditions to be convex simultaneously. Furthermore, by comparing with the existing methods, this method not only can eliminate the binding to the input matrix B, but also is able to provide a wider range of stability region. Besides, to enhance the relaxation of the stability analysis, we introduce the up-to-date Taylor series membership functions (TSMFs) approximation method such that the information embedded in the membership functions and the state boundary information can be taken into the stability conditions. As a result, on the strength of Lyapunov stability theory, the stability analysis is performed via sum-of-squares (SOS) approach. Finally, a simulation example is given to illustrate the effectiveness and reliability of the proposed method.