A Novel Piecewise Affine Filtering Design for T–S Fuzzy Affine Systems Using Past Output Measurements

This paper tackles the problem of piecewise affine memory filtering design for the discrete-time norm-bounded uncertain Takagi–Sugeno fuzzy affine systems. The objective is to design an admissible filter using past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a given
${\mathscr H}_{\infty }$
performance index. Based on the piecewise fuzzy Lyapunov functions and the projection lemma, a new sufficient condition for
$\mathscr H_{\infty }$
filtering performance analysis is first derived, and then the filter synthesis is carried out. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities. In addition, it is also shown that the filtering performance can be improved with the increasing number of past output measurements used in the filtering design. Finally, two examples are presented to show the advantages and effectiveness of the proposed approach.