Robust Stabilization for Discrete Uncertain Takagi–Sugeno Fuzzy Systems Based on a Piecewise Lyapunov Function

Abstract

This article investigates the robust H∞ fuzzy output-feedback control problem for a discrete Takagi–Sugeno (T–S) fuzzy system with uncertainties. By constructing a discrete piecewise Lyapunov function in each maximal overlapped-rule group, the systematic design of the fuzzy robust H∞ controller is studied through the parallel distributed compensation control scheme, and a new sufficient condition to check the robust asymptotic stabilization of the closed-loop discrete uncertain T–S fuzzy system is proposed and confirmed. This sufficient condition requires only finding common matrices in each maximal overlapped-rule group. Compared with the common Lyapunov function approach and the fuzzy Lyapunov function approach, the proposed sufficient condition can not only overcome the defect of finding common matrices in the whole feasible region but also significantly reduce the number of linear matrix inequalities to be solved. Therefore, the proposed condition is less conservative and difficult than the other two approaches. Finally, the simulation results for a class of two-echelon uncertain nonlinear supply chain systems show the effectiveness of the proposed approach.