The design of robust H∞ filtering problem of polytopic uncertain linear timedelay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameterdependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H∞ performance level for all admissible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. An extended H∞ sufficient condition for the existence of robust estimators is formulated in terms of linear matrix inequalities, which can be solved via efficient interiorpoint algorithms. The design of robust H∞ filtering problem of polytopic uncertain linear timedelay systems is addressed. The uncertainty parameters are supposed to reside in a polytope. A parameterdependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H∞ performance level for all admissible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain. This idea is realized by carefully selects the structure of the matrices involved in the products with system matrices. An extended H∞ sufficient condition for the existence of robust estimators is formulated in terms of linear matrix inequalities, which can be solved via efficient interiorpoint algorithms.