A lowerbound on the dimension of positive realizations

Nagy, Béla and Matolcsi, Máté (2003) A lowerbound on the dimension of positive realizations. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I - FUNDAMENTAL THEORY AND APPLICATIONS, 50 (6). pp. 782-784. ISSN 1057-7122


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A basic phenomenon in positive system theory is that the dimension N of an arbitrary positive realization of a given transfer function H(z) may be strictly larger than the dimension n of its minimal realizations. The aim of this brief is to provide a non-trivial lower bound on the value of N under the assumption that there exists a time instant k0 at which the (always nonnegative) impulse response of H(z) is 0 but the impulse response becomes strictly positive for all k > k0. Transfer functions with this property may be regarded as extremal cases in positive system theory.

Item Type: Article
Uncontrolled Keywords: System theory; VECTORS; Transfer functions; Matrix algebra; Linear systems; estimation; Positive realization; Positive linear systems; Dimension estimates; Reachability; SYSTEMS
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: MTMT SWORD
Date Deposited: 10 Dec 2013 14:34
Last Modified: 10 Dec 2013 14:49

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