This note deals with the problem of full-order observer design for linear, descriptor systems with unknown input (UI) and time-varying delays. The resulting filter is of Luenberger observer type, and it guarantees that the Hinf-norm of the system, relating the exogenous signals to the estimation error, is less than a prescribed level. Four slack matrix variables are introduced in the derivative of the Lyapunov functional in order to reduce conservatism in existing delay dependent stability conditions. Both delay-dependent and delay-independent criteria are obtained. The applicability of the proposed approach is shown through a numerical example.