Connection between plant zeros and H∞ controller order reduction

Abstract

The phenomenon of H^∞ controller-pole/plant-zero cancellation is analyzed. Symmetrical descriptor form formulae for the H^∞ central controller are derived and are used to prove controller-pole/plant-zero cancellation in H^∞ design. It is also shown that these particular controller poles are not controllable/observable from the auxiliary compensator/free parameter. This fact is then exploited to find an auxiliary compensator which will produce an internal pole-zero cancellation of s_o within the H^∞ controller, reducing the order of the controller without affecting the closed loop H^∞ norm.