Full and Reduced-Order H∞ Filtering of Takagi–Sugeno Fuzzy Time-Varying Delay Systems: Input–Output Approach

This article addresses the issue of delay-dependent H∞ filtering design for TakagiŮSugeno fuzzy time-varying delay systems using the input–output approach. A three-term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function s (MF) time derivative, upper-bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time-derivative, the H∞ full- and reduced-order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods. © 2021 John Wiley & Sons, Ltd.