Stability of discrete fuzzy systems with nontriangular membership functions

We present new results for the stability analysis of discrete dynamic fuzzy systems with nontriangular membership functions. We use arguments similar to those applied to the stability analysis of systems with triangular membership functions, including: the concept of fuzzy positive definite and fuzzy negative definite functions. We use a fuzzy Lyapunov function candidate with triangular membership functions to derive the new stability conditions for systems with nontriangular membership functions. We apply our results to two numerical examples.