TY - GEN A1 - Reis, Timo T1 - Lur'e Equations and Even Matrix Pencils N2 - In this work we consider the so-called Lur'e matrix equations that arise e.g. in model reduction and linear-quadratic infinite time horizon optimal control. We characterize the set of solutions in terms of deflating subspaces of even matrix pencils. In particular, it is shown that there exist solutions which are extremal in terms of definiteness. It is shown how these special solutions can be constructed deflating subspaces of even matrix pencils. KW - Lur'e equations KW - Riccati equations KW - optimal control KW - spectral factorization KW - deflating subspaces KW - even matrix pencils Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/667 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6677 ER -