TY - JOUR
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
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=57949111758&partnerID=8YFLogxK
U2 - 10.1109/TCSII.2008.2003344
DO - 10.1109/TCSII.2008.2003344
M3 - Artículo
AN - SCOPUS:57949111758
SN - 1549-7747
VL - 55
SP - 1203
EP - 1207
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
IS - 11
ER -