SYNTHESIS OF PROPORTIONAL-PLUS-DERIVATIVE FEEDBACKS FOR DESCRIPTOR SYSTEMS

Construction for proportional-plus-derivative (PD) feedbacks for descriptor (or singular) systems is given. It is shown that, under the assumption of controllability of the open-loop finite and (dynamic) infinite modes, feedbacks employing states and state derivatives may be constructed to accomplish shifting all open-loop modes (finite as well as infinite) to desired finite points while ensuring regularity of the closed-loop pencils. Further, the construction reveals that the required state-derivative feedbacks are specified completely by the open-loop dynamic infinite-mode structures of the descriptor systems. This class of PD feedbacks circumvents certain difficulties associated with the construction for constant state-feedbacks as given by Armentano, by Lewis, and by Fletcher and co-workers.