Discrete-time Adaptive Regulation of Scalar Systems with Uncertain Upper-bounded Input Delay

This paper proposes a discrete-time adaptive regulator for a scalar, linear time-invariant system with an unknown, constant input time delay that has a known upper-bound. The main contributions of this work are: 1) this is achieved without explicitly estimating the time delay, and 2) neither the plant nor its discretised model are required to have stable open-loop zeros. To cope with the unknown time delay, the control and adaptive laws are structured to accommodate use of control history data for a duration extending as far back as the delay upper-bound. A stability analysis shows that the proposed regulator drives the plant state to zero asymptotically and simulation results are shown to verify the approach.