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A note on minimality of positive realizations

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2 Author(s)
L. Benvenuti ; Dipartimento di Inf. e Sistemistica, Rome Univ., Italy ; L. Farina

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 work 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

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IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications  (Volume:45 ,  Issue: 6 )