Simplifications and clarifications on the paper ´An algebra of transfer functions for distributed linear time-invariant systems´

Author

Callier, F. ; Desoer, C.

Volume

Issue

fYear

1980

fDate

4/1/1980 12:00:00 AM

Firstpage

320

Lastpage

323

Abstract

In this note we first point out some simplifications in some results of our paper mentioned above [1]. Second, we prove that the algebra of transfer functions $\\hat{cal B}(\\sigma _0)$ , introduced in the paper, is in fact the quotient ring of the ring $\\hat{\\cal Q}_{\\_}(\\sigma _0)$ with respect to the multiplicative system $\\hat{\\cal Q}_{\\_}^{\\infty } (\\sigma _0)$ defined in this note. The analogy between $\\hat{cal B}(\\sigma _0)$ , seen as the quotient $[\\hat{\\cal Q}_{\\_}(\\sigma _0)][\\hat{\\cal Q}_{\\_}^{\\infty } (\\sigma _0)]^{-1}$ , and the algebra of proper rational functions $C_p (s)$ seen as the quotient $[\\Re (\\sigma _0)][\\Re ^{\\infty } (\\sigma _0)]^{-1}$ (where $\\Re _0 (\\sigma _0 )$ is the ring of proper rational functions analytic in $\\Re s \\geq \\sigma _0$ , and $\\Re ^{\\infty } (\\sigma _0)$ is the multiplicative system of such functions tending to a nonzero constant as $|s| i\\rightarrow \\infty$ ), is fully developed and supports the claim that $\\hat{cal B} (\\sigma _0 )$ is a natural extension of the algebra of proper rational functions to distributed systems. These algebraic developments have been found most useful in applications [11], [12].

Keywords

Algebra; Distributed systems, linear time-invariant; Interconnected systems; Transfer functions; Algebra; Circuit theory; Digital filters; Distributed parameter circuits; Equivalent circuits; Limit-cycles; Solid modeling; Transfer functions; Transmission line theory; Transmission lines;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1980.1084802

Filename

1084802

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1183550