Minimal positive realizations of transfer functions with nonnegative multiple poles

Nagy, B. and Matolcsi, Máté (2005) Minimal positive realizations of transfer functions with nonnegative multiple poles. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 50 (9). pp. 1447-1450. ISSN 0018-9286


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This note concerns a particular case of the minimality problem in positive system theory. A standard result in linear system theory states that any nth-order rational transfer function of a discrete time-invariant linear single-input-single-output (SISO) system admits a realization of order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e., a positive system), and it is known that this restriction may force the order N of realizations to be strictly larger than n. A general solution to the minimality problem (i.e., determining the smallest possible value of N) is not known. In this note, we consider the case of transfer functions with nonnegative multiple poles, and give sufficient conditions for the existence of positive realizations of order N = n. With the help of our results we also give an improvement of an existing result in positive system theory.

Item Type: Article
Uncontrolled Keywords: Control Theory; Single-input-single-output (SISO) system; Mcmillan degree; Transfer functions; Poles and zeros; Optimization; Mathematical models; Linear control systems; iterative methods; Discrete time control systems; Positive linear systems; Minimal realizations; Discrete-time filtering; SYSTEMS
Subjects: Q Science / természettudomány > QA Mathematics / matematika
T Technology / alkalmazott, műszaki tudományok > TA Engineering (General). Civil engineering (General) / általános mérnöki tudományok
T Technology / alkalmazott, műszaki tudományok > TK Electrical engineering. Electronics Nuclear engineering / elektrotechnika, elektronika, atomtechnika
Depositing User: MTMT SWORD
Date Deposited: 10 Dec 2013 13:50
Last Modified: 10 Dec 2013 13:50

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