Interval observers for continuous-time linear systems with discrete-time outputs

We consider continuous-time linear systems with additive disturbances and discrete-time measurements. First, we construct an observer, which converges to the state trajectory of the linear system when the maximum time interval between two consecutive measurements is sufficiently small and there are no disturbances. Second, we obtain interval observers allowing one to determine, for any solution, a set that is guaranteed to contain the actual state of the system when bounded disturbances are present.