Gain and phase margin of optimal memoryless regulator of systems with time-delay

Abstract

A class of linear quadratic regulators of the system with time-delay in the states is constructed by a memoryless feedback, and its robustness is evaluated. First, a static non-linear perturbation is inserted in the input channel, and a robust stability condition is derived. As its special case, it is shown that the regulator has infinite gain margin and at least 50% gain reduction tolerance. Next, a dynamic linear perturbation is inserted in the same point, and an alternative stability condition is derived. It assures that the regulator has at least 60o phase margin. These results coincide with those of the finite dimensional LQ regulator.