Impulsive set-membership state estimators for continuous-time linear systems based on delayed discrete-time periodic measurements

This work proposes the use of explicit reachability analysis of the estimation error to design an impulsive set-valued state estimator for continuous-time linear systems, where the measurements are available at discrete-time instants and delayed. The introduced state estimator combines two procedures of state estimation in the set-valued paradigm. The first one is an open loop prediction phase, where the measurements are not required, while the second one is a discrete-time correction phase based on the available measurements. In addition, under the detectability assumption of a discrete-time form of the continuous-time system, the practical convergence of the estimation error is demonstrated. A numerical example borrowed from the literature is considered, to support the theoretical results.