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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.>
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V.X. Le (1992) studied this question.
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