Stability analysis of discrete T-S Fuzzy Systems

Based on the properties of fuzzy systems with two-overlapped fuzzy partition inputs, the stability analysis of discrete T-S fuzzy systems is discussed. First, a new piecewise discrete Lyapunov function is constructed in maximal overlapped-rule group. Each discrete Lyapunov function lies in its own operating regions of maximal overlapped-rule group. And then based on this a new sufficient condition to check the stability of the open-loop system is proposed. This condition only requires finding a common positive-definite matrix in each maximal overlapped-rule group. Compared with former stability analysis approaches, it can not only overcome the defect of finding a common positive-definite matrix but also reduce the number of solving Lyapunov inequalities. At last, a simulation example shows that the method is effective and advantageous.