<p>In this work, we use reachability analysis as the core stone to design secure state estimator for controlled continuous-time linear systems. First, an augmented model that includes the dynamics of the estimation error is established. Then, based on this model, we introduce a new explicit method for reachability analysis of closed-loop systems. Thereafter, using the results of this method, we propose set-membership tests to detect the presence of faults or stealthy attacks on the system sensors and actuators. To show the effectiveness of the proposed approach, we consider a numerical example illustrating the ability of the introduced set-valued state estimator to detect system anomalies.</p>