Stabilization of delayed linear systems via signal reconstruction

This work addresses the problem of time varying delays in systems and control. In the first part of the paper, we propose a processing scheme that allows reconstruction of a signal subject to time-varying delays. We show robustness of the scheme with respect to sensing and actuation noise. We obtain a necessary and sufficient result for stability of compensated scalar linear systems under constant time delay. Then we apply the scheme to a general n dimensional linear system subject to time-varying delay in the state feedback. We present sufficient conditions for stability of the closed loop system. These conditions provide a constructive procedure to design the compensation parameter to maximize the delay that the system can support, while remaining stable.