Finite Frequency $L_{2}{-}L_{\infty }$ Filtering of T-S Fuzzy Systems With Unknown Membership Functions

Abstract

This paper is concerned with the problem of finite frequency ${L}_{{2}}{-}{L}_{\infty }$ filtering for Takagi-Sugeno fuzzy systems with unknown membership functions. An ${L}_{{2}}{-}{L}_{\infty }$ performance index is first defined in finite frequency domain from the signal’s point of view. By using matrix trace calculations, a new result based on ${L}_{{2}}{-}{L}_{\infty }$ performance analysis is derived in finite frequency range. Moreover, a design criterion of the desired finite frequency filter with varying gains is given in terms of a set of linear matrix inequalities and switching laws. It is shown that the proposed finite frequency filtering method can achieve better filtering performance than the existing full frequency ones. Finally, two simulation examples are introduced to verify the theoretical results.