title: Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach.
abstract: This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.
authors.forename: Xiangpeng
authors.initials: X
authors.lastname: Xie
authors.forename: Dong
authors.initials: D
authors.lastname: Yue
authors.forename: Tiedong
authors.initials: T
authors.lastname: Ma
authors.forename: Xunlin
authors.initials: X
authors.lastname: Zhu