Traditional model-based approaches are based on periodic iterations, where the continuous-time model is discretized with a fixed period. Despite the easiness in analysis and design, such periodic approximation model may be undesirable from the computation-efficiency point of view. This paper presents the Lebesgue-approximation model (LAM) of continuous-time nonlinear systems, where the iteration is activated on an "as-needed" basis, but not periodically. We show that the proposed LAM behaves exactly the same as a specific event-triggered feedback system, through which the properties of the LAM can be studied. We provide a sufficient condition to ensure asymptotic stability of the LAM and derive theoretical bounds on the difference between the states of the LAM and the original continuous-time system. The LAM is then integrated in the particle-filtering approach for fault prognosis. Simulation results show that the LAM can dramatically reduce the number of iterations in prognosis without sacrificing accuracy and precision. (C) 2015 Elsevier Ltd. All rights reserved.