Stability Analysis of Discrete T-S Fuzzy Systems with Standard Fuzzy Partition Inputs

The stability analysis of discrete T-S fuzzy systems is discussed in this paper. First, a piecewise discrete Lyapunov function is constructed in all maximal overlapped-rule groups. Each discrete Lyapunov function lies in its own maximal overlapped-rule group. Then, a new sufficient condition to check the stability of discrete T-S fuzzy systems is proposed. This condition only requires finding a common positive definite matrix in each maximal overlapped-rule group. Compared with former stability analysis approaches, this approach can not only overcome the defect of finding a common positive definite matrix but also reduce the number of solving Lyapunov inequalities largely. At last, a simulation example shows the approach is effective