Abstract—A well-known result from linear system theory states that the minimal inner size of a factorization of the Hankel matrix H of a system gives the minimal order of a realization. In this brief it is shown that when dealing with positive linear systems, the existence of a factorization of the Hankel matrix into two nonnegative matrices is only a necessary condition for the existence of a positive realization of order equal to the inner size of the factorization. Necessary and sufficient conditions for the minimality of a positive realization in terms of positive factorization of the Hankel matrix are then derived.
A note on minimality of positive realizations / Benvenuti, Luca; Farina, Lorenzo. - In: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I. FUNDAMENTAL THEORY AND APPLICATIONS. - ISSN 1057-7122. - 45:6(1998), pp. 676-677. [10.1109/81.678491]
A note on minimality of positive realizations
BENVENUTI, Luca;FARINA, Lorenzo
1998
Abstract
Abstract—A well-known result from linear system theory states that the minimal inner size of a factorization of the Hankel matrix H of a system gives the minimal order of a realization. In this brief it is shown that when dealing with positive linear systems, the existence of a factorization of the Hankel matrix into two nonnegative matrices is only a necessary condition for the existence of a positive realization of order equal to the inner size of the factorization. Necessary and sufficient conditions for the minimality of a positive realization in terms of positive factorization of the Hankel matrix are then derived.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
