H∞ Control for Discrete-Time Fuzzy Descriptor Systems

This paper investigates the problem of H_infin control for T-S fuzzy discrete-time descriptor systems. Firstly, an analysis result for H_infin control is derived and characterized by a set of linear matrix inequalities (LMIs). The derived analysis condition is then applied to design an H_infin fuzzy controller. In T-S fuzzy discrete-time descriptor systems, due to singularity of E-matrix, Schur complement cannot be applied to solve the nonlinear Lyapunov inequality anymore for H_infin control. The difficulty is overcome by the approach proposed in this paper. Before this presentation, no result about the H_infin control of T-S fuzzy discrete-time descriptor systems is available in the literature, the paper seems the first one to tackle it from the theoretical aspect.