The Principle of “Borrowed Feedback” and Application to Control and Observation for Systems with Varying Delay

This short paper first explains the general principle of “borrowed feedback” for linear systems with constant input delay, and in its dual form of observation with delayed measurements. This is of interest in problems where the external interaction with the system incurs a delay. One application is the control of systems over a network. In this case the delay cannot be considered constant, but depends on a congestion state of the network. It is shown that if the causality constraint, which imposes an upper bound on the rate of change of the delay, does not hold the design method fails to give consistent results.