Stabilization strategy for unstable first order linear systems with large time-delay

This work considers the problem of stabilization of a class of unstable first order linear systems subject to a large input-output time delay. Necessary and sufficient conditions are stated to guarantee the stability of the closed loop delayed system by means of a compensation scheme based on two static gains and an induced delay term. The proof of the main result is derived by considering a discrete time approach that, under adequate assumptions, allows to conclude the stability condition for the continuous time case.