Interval Observers for Linear Systems with Time-Varying Delays

This paper considers linear observed systems with time-varying delays, where the state as well as the observation of the state is subject to delays. It is assumed that the delays are unknown but stay below a certain bound. Similar to the case of uncertainties in the systems parameters we aim to derive upper and lower estimates for the state of the system under consideration. A pair of estimators providing such bounds is called an interval observer. In particular, the case where the estimators converge asymptotically is of notable interest. In this case the interval observer is said to be convergent. In this paper we derive necessary and sufficient conditions for the existence of a convergent interval observer for linear observed systems with time-varying bounded delays.