In this paper we show how, by extending a classical Lemma due to Dayawansa, it is possible to enhance the theory of robust extended observers so as to cover a wide class of nonlinear systems, namely those systems whose normal form is characterized by "time-dependent gains" in the "string of integrators between input and output". Such class includes helicopters, quadrotors, robot arms and electric drives. (C) 2019 Elsevier Ltd. All rights reserved.