Admissibility and admissibilization for T–S fuzzy descriptor systems with partially unknown membership functions

Abstract

In this paper, the admissibility analysis and controller design issues for a class of nonlinear descriptor systems described by the T–S descriptor fuzzy model with partially unknown membership functions are discussed. New sufficient conditions are first given to ensure the admissibility of such fuzzy descriptor systems. To fully utilise the information of membership functions, the known and unknown parts of membership functions are handled by staircase functions and the bounds of the unknown part, respectively. Different from the traditional parallel distribution compensation (PDC) method, the state-feedback controller design condition is given under an imperfect premise matching method via linear matrix inequalities (LMIs). Some examples are given to show the validity of the proposed methods.