A signal reconstruction approach for control systems with unknown time-varying delays

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 nn 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. Finally, we extend the scheme to delayed nonlinear systems and prove stability of the closed loop system for proper values of the control parameter.