On realization of left and right products of rational functions

Daniel Alpay; Izchak Lewkowicz

doi:10.1016/j.laa.2023.02.015

On realization of left and right products of rational functions

Daniel Alpay
, Izchak Lewkowicz

Department of Electrical & Computer Engineering

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

Abstract

Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations between state-space realization of two pairs of functions: The original functions F and G, and on the other hand both of their products FG and GF. Motivated by the structure of asymmetric communication channels, we show how from the realization of the products FG and GF, one can explicitly recover the realizations of F and G.

Original language	English
Pages (from-to)	42-61
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	666
DOIs	https://doi.org/10.1016/j.laa.2023.02.015
State	Published - 1 Jun 2023

Keywords

Factorization
Spectral factorization
State-space realization

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2023.02.015

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abstract = "Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations between state-space realization of two pairs of functions: The original functions F and G, and on the other hand both of their products FG and GF. Motivated by the structure of asymmetric communication channels, we show how from the realization of the products FG and GF, one can explicitly recover the realizations of F and G.",

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AU - Lewkowicz, Izchak

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N2 - Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations between state-space realization of two pairs of functions: The original functions F and G, and on the other hand both of their products FG and GF. Motivated by the structure of asymmetric communication channels, we show how from the realization of the products FG and GF, one can explicitly recover the realizations of F and G.

AB - Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations between state-space realization of two pairs of functions: The original functions F and G, and on the other hand both of their products FG and GF. Motivated by the structure of asymmetric communication channels, we show how from the realization of the products FG and GF, one can explicitly recover the realizations of F and G.

KW - Factorization

KW - Spectral factorization

KW - State-space realization

UR - https://www.scopus.com/pages/publications/85148901480

U2 - 10.1016/j.laa.2023.02.015

DO - 10.1016/j.laa.2023.02.015

M3 - Article

AN - SCOPUS:85148901480

SN - 0024-3795

VL - 666

SP - 42

EP - 61

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On realization of left and right products of rational functions

Abstract

Keywords

ASJC Scopus subject areas

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