Observer design of discrete-time T–S fuzzy systems via multi-instant augmented multi-indexed matrix approach

Abstract

The problem of relaxed observer design for discrete-time Takagi–Sugeno (T–S) fuzzy systems is addressed in this paper. With the framework of improved homogenous matrix polynomials, a novel kind of slack variable approach, which is homogenous polynomially parameter-dependent on multi-instant normalized fuzzy weighting functions with arbitrary degrees, is proposed by developing an efficient multi-instant augmented multi-indexed matrix approach. Since the algebraic properties of multi-instant normalized fuzzy weighting functions are collected into a set of augmented multi-indexed matrices, more information about multi-instant normalized fuzzy weighting functions can be involved into observer design. As a result, the relaxation quality of fuzzy observer design can be significantly improved. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.