Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles

Luca Benvenuti; Larenzo Farina; Brian Anderson; Franky De Bruyne

Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles

Luca Benvenuti, Larenzo Farina, Brian Anderson, Franky De Bruyne

School of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A standard result of linear system theory states that a SISO rational n-th order transfer function always has a n-th order realization. In some applications one is interested in having a realization with nonnegative entries (i.e. a positive system). In this paper we give a contribution to the discrete-time realization problem by providing explicit necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization. The conditions are easily testable and the proof is constructive so that it is straighforward to obtain a minimal positive realization.

This paper is the 1st version of 'Minimal Positive Realizations of Transfer Functions With Real Poles', 2000 https://doi.org/10.1109/TAC.2012.2212612

Original language	English
Title of host publication	Proceedings of the 1998 International Symposium on Mathematical Theory of Networks and Systems, MTNS 98
Pages	81-84
Publication status	Published - 1998
Event	Mathematical Theory of Networks and Systems Symposium (MTNS-98) - Padova, Italy Duration: 6 Jul 1998 → 10 Jul 1998

Conference

Conference	Mathematical Theory of Networks and Systems Symposium (MTNS-98)
Abbreviated title	MTNS-98
Country/Territory	Italy
City	Padova
Period	6/07/98 → 10/07/98

Cite this

@inproceedings{10239a8c72b64d1296ef1f08b1edd2c9,

title = "Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles",

abstract = "A standard result of linear system theory states that a SISO rational n-th order transfer function always has a n-th order realization. In some applications one is interested in having a realization with nonnegative entries (i.e. a positive system). In this paper we give a contribution to the discrete-time realization problem by providing explicit necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization. The conditions are easily testable and the proof is constructive so that it is straighforward to obtain a minimal positive realization.This paper is the 1st version of 'Minimal Positive Realizations of Transfer Functions With Real Poles', 2000 https://doi.org/10.1109/TAC.2012.2212612",

author = "Luca Benvenuti and Larenzo Farina and Brian Anderson and {De Bruyne}, Franky",

year = "1998",

language = "English",

pages = "81--84",

booktitle = "Proceedings of the 1998 International Symposium on Mathematical Theory of Networks and Systems, MTNS 98",

note = "Mathematical Theory of Networks and Systems Symposium (MTNS-98), MTNS-98 ; Conference date: 06-07-1998 Through 10-07-1998",

}

Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles. / Benvenuti, Luca; Farina, Larenzo; Anderson, Brian et al.
Proceedings of the 1998 International Symposium on Mathematical Theory of Networks and Systems, MTNS 98. 1998. p. 81-84.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles

AU - Benvenuti, Luca

AU - Farina, Larenzo

AU - Anderson, Brian

AU - De Bruyne, Franky

PY - 1998

Y1 - 1998

N2 - A standard result of linear system theory states that a SISO rational n-th order transfer function always has a n-th order realization. In some applications one is interested in having a realization with nonnegative entries (i.e. a positive system). In this paper we give a contribution to the discrete-time realization problem by providing explicit necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization. The conditions are easily testable and the proof is constructive so that it is straighforward to obtain a minimal positive realization.This paper is the 1st version of 'Minimal Positive Realizations of Transfer Functions With Real Poles', 2000 https://doi.org/10.1109/TAC.2012.2212612

AB - A standard result of linear system theory states that a SISO rational n-th order transfer function always has a n-th order realization. In some applications one is interested in having a realization with nonnegative entries (i.e. a positive system). In this paper we give a contribution to the discrete-time realization problem by providing explicit necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization. The conditions are easily testable and the proof is constructive so that it is straighforward to obtain a minimal positive realization.This paper is the 1st version of 'Minimal Positive Realizations of Transfer Functions With Real Poles', 2000 https://doi.org/10.1109/TAC.2012.2212612

UR - https://www.researchgate.net/publication/2341660_Minimal_Discrete-Time_Positive_Realizations_of_Transfer_Functions_With_Positive_Real_Poles

M3 - Conference contribution

SP - 81

EP - 84

BT - Proceedings of the 1998 International Symposium on Mathematical Theory of Networks and Systems, MTNS 98

T2 - Mathematical Theory of Networks and Systems Symposium (MTNS-98)

Y2 - 6 July 1998 through 10 July 1998

ER -

Minimal Discrete-Time Positive Realizations of Transfer Functions With Positive Real Poles

Abstract

Conference

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