In this paper we begin by assuming that an observer with a corresponding quadratic-type Lyapunov function has been designed for a given nonlinear system. We then consider the problem that arises when the output of that nonlinear system is not directly available; instead, it acts as an input to a second, linear system from which a partial-state measurement is in turn available. We develop an observer design methodology for the resulting cascade interconnection, based on estimating the unavailable output together with the states of the linear system. We also extend this methodology to a more general class of feedback-interconnected systems. Under a set of technical assumptions, the overall error dynamics is proven to be globally exponentially stable if the gains are chosen to satisfy an H-infinity condition. We illustrate application of the methodology by considering a navigation example based on integration of inertial and satellite measurements. (C) 2012 Elsevier Ltd. All rights reserved.