Synthesis of proportional-plus-derivative feedbacks for descriptor systems

A construction for proportional-plus-derivative (PD) feedback 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, feedback employing states and state derivatives can be constructed to shift all open-loop modes (finite as well as infinite) to desired finite points while ensuring the regularity of the closed-loop pencils. The construction reveals that the required state-derivative feedback is specified completely by the open-loop dynamic infinite-mode structures of the descriptor systems. This class of PD feedback circumvents certain difficulties associated with the construction for constant state-feedback