'Delay scheduling', an unconventional use of time delay for trajectory tracking

A basic trajectory tracking exercise is conducted on a linear time invariant (LTI) dynamics with a fixed control law. The feedback considered here, however, is affected by a time delay, τ, which maybe uncertain. Interestingly, time delayed LTI systems may exhibit multiple stable operating regions in the space of the delay. However, systematic, exact and exhaustive determination of these regions is, mathematically speaking, still a challenging problem. The contribution of this paper is three fold. First, to deploy a recent framework called Cluster Treatment of Characteristic Roots (CTCR) and experimentally verify the stability regions. Second, to establish an unconventional control law, called the "delay scheduling" procedure, to use the time delay as a control parameter. Third, to determine the best ("optimum" in certain respect) time delay value(s) rendering the most desirable tracking characteristics.