Extension of Kalman–Yakubovich–Popov lemma to descriptor systems

This paper presents a complete analogue of the well-known Kalman–Yakubovich–Popov lemma for descriptor systems, i.e. necessary and sufficient linear matrix inequality conditions for passivity and positive realness of descriptor systems. Also a full characterization of extended strictly positive realness is given for this class of systems. Some of the earlier related results are recovered from the presented results.