A standard result of linear system theory states that an SISO proper rational transfer function of degree n always has a realization of dimension n. In some applications one is interested in having a realization with nonnegative entries and it is known that, when the dominant poles display a specic pattern, forcing nonnegativity leads to a system which is not jointly reachable and observable. In this paper, we show that the minimal dimension of a positive realization may be `large' even in the case of a single dominant pole. More precisely, we provide a family of transfer functions, each of which is of degree n=3, such that for any integer N>3 the corresponding member of the family admits a minimal positive realization of state space dimension not smaller than N.

An example of how positivity may force realizations of 'large' dimension / Benvenuti, Luca; Farina, Lorenzo. - In: SYSTEMS & CONTROL LETTERS. - ISSN 0167-6911. - 36(1999), pp. 261-266. [10.1016/S0167-6911(98)00098-X]

An example of how positivity may force realizations of 'large' dimension

BENVENUTI, Luca;FARINA, Lorenzo
1999

Abstract

A standard result of linear system theory states that an SISO proper rational transfer function of degree n always has a realization of dimension n. In some applications one is interested in having a realization with nonnegative entries and it is known that, when the dominant poles display a specic pattern, forcing nonnegativity leads to a system which is not jointly reachable and observable. In this paper, we show that the minimal dimension of a positive realization may be `large' even in the case of a single dominant pole. More precisely, we provide a family of transfer functions, each of which is of degree n=3, such that for any integer N>3 the corresponding member of the family admits a minimal positive realization of state space dimension not smaller than N.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/245242
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 32
social impact