Abstract: In this paper, a novel direct design methodology of robust fault detection for a class of sampled-data systems with both continuous-time process noise and discrete-time measurement noise is presented. First, by using a linear system with finite discrete jumps as residual generator, the design of robust fault detection filter is formulated as a sampled-data filtering problem. Then, a bounded real lemma for the linear system with finite discrete jumps is developed in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition for the existence of the fault detection filter as well as the design parameters is derived. Furthermore, the case of sampled-data systems with model uncertainties is extended. The designed fault detection filter cannot only make the error between residual and weighted fault as small as possible but also exhibit robustness to all uncertainties including continuous-time process noise, discrete-time measurement noise, and model uncertainties. Finally, simulation results are provided to demonstrate the feasibility of the proposed method.