Stabilizing Rational Controllers for a Class of a Time-Delay Systems

Abstract

The problem of stabilization of a linear system characterized by its rational transfer function, with an input time delay, by a rational controller, is considered. If the delay is not known at all (its interval is infinite), it is proved that the necessary and sufficient condition for the existence of a rational controller is stability of the open loop rational plant. Moreover, the existence of a rational stabilizing controller implies the existence of a constant gain stabilizing controller. If the delay is known to lie in a given finite interval, two non-existence theorems are derived, one for the constant gain stabilizing controller and one for any rational stabilizing controller. Design method based on first order all-pass filters cascaded by a constant gain is presented.