On operators on positive real functions and related issues

Guillermo Fernández-Anaya; Baltazar Aguirre; Rodolfo Suárez; José Job Flores-Godoy

doi:10.1109/TCSII.2008.2003344

On operators on positive real functions and related issues

Guillermo Fernández-Anaya, Baltazar Aguirre, Rodolfo Suárez, José Job Flores-Godoy

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we proved that the sets of strict positive real functions with zero relative degree (SPR0) and positive real (PR) single-input--single-output functions are closed under linear operators preserving stability and for rational functions by differentiation of the numerator and denominator. Also, we show that any PR system can be approximated by an SPR0 system. These results are extended to strict bounded real and bounded real functions when the numerator and denominator polynomials are transformed by a class of linear operators. Additionally, for functions in RH∞, the H∞-norm is preserved under linear operators applied on numerator and denominator polynomials. Three possible applications are given.

Original language	English
Pages (from-to)	1203-1207
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems II: Express Briefs
Volume	55
Issue number	11
DOIs	https://doi.org/10.1109/TCSII.2008.2003344
State	Published - 2008
Externally published	Yes

Keywords

Bounded real (BR) functions
Linear operators
Positive real (PR) functions
Strict bounded real (SBR) functions
Strict positive real (SPR) functions

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10.1109/TCSII.2008.2003344

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T1 - On operators on positive real functions and related issues

AU - Fernández-Anaya, Guillermo

AU - Aguirre, Baltazar

AU - Suárez, Rodolfo

AU - Flores-Godoy, José Job

PY - 2008

Y1 - 2008

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AB - In this paper, we proved that the sets of strict positive real functions with zero relative degree (SPR0) and positive real (PR) single-input--single-output functions are closed under linear operators preserving stability and for rational functions by differentiation of the numerator and denominator. Also, we show that any PR system can be approximated by an SPR0 system. These results are extended to strict bounded real and bounded real functions when the numerator and denominator polynomials are transformed by a class of linear operators. Additionally, for functions in RH∞, the H∞-norm is preserved under linear operators applied on numerator and denominator polynomials. Three possible applications are given.

KW - Bounded real (BR) functions

KW - Linear operators

KW - Positive real (PR) functions

KW - Strict bounded real (SBR) functions

KW - Strict positive real (SPR) functions

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JO - IEEE Transactions on Circuits and Systems II: Express Briefs

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On operators on positive real functions and related issues

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