Full and reduced‐order <i>H</i><sub><i>∞</i></sub> filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach
Hicham El Aiss, Taha Zoulagh, Ahmed El Hajjaji, Abdelaziz Hmamed
Abstract
Summary 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.