TY - GEN A1 - Mehrmann, Volker A1 - Nabben, Reinhard A1 - Virnik, Elena T1 - Generalisation of the Perron-Frobenius theory to matrix pencils N2 - We present a new extension of the well-known Perron-Frobenius theorem to regular matrix pairs $(E,A)$. The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied. KW - Perron-Frobenius theorem KW - matrix pencils KW - differential-algebraic equation KW - descriptor system KW - projector chain KW - tractability index KW - differentiation index Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/374 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3741 ER -