Stability analysis for T-S fuzzy control systems with linear interpolations into membership functions

This paper focuses on the stability analysis of T-S fuzzy control systems. The artificial T-S model method is utilized with piecewise linear interpolations into the normalized fuzzy membership functions. The stability conditions are derived to a series of LMIs. Using piecewise linear interpolation functions, we obtain finite LMIs and only solve them at the interpolation points. Furthermore, because of the dramatically improved approximation accuracy of piecewise linear interpolations, the method presented in this paper can provide a wider stable region for T-S fuzzy control systems, compared with the approach with staircase (zero-order) interpolations. A simulation example is adopted to illustrate the advantage of the proposed method.