Composition of rational functions: State-space realization and applications

Daniel Alpay; Izchak Lewkowicz

doi:10.1016/j.laa.2019.06.014

Composition of rational functions: State-space realization and applications

Daniel Alpay, Izchak Lewkowicz

Department of Electrical & Computer Engineering

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

3 Scopus citations

Abstract

We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.

Original language	English
Pages (from-to)	359-383
Number of pages	25
Journal	Linear Algebra and Its Applications
Volume	580
DOIs	https://doi.org/10.1016/j.laa.2019.06.014
State	Published - 1 Nov 2019

Keywords

Composition
Convex invertible cones
Electrical circuits
Feedback loops
Positive real functions
Rational functions of non-commuting variables
State-space realization
Stieltjes functions

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.2019.06.014

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title = "Composition of rational functions: State-space realization and applications",

abstract = "We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.",

keywords = "Composition, Convex invertible cones, Electrical circuits, Feedback loops, Positive real functions, Rational functions of non-commuting variables, State-space realization, Stieltjes functions",

author = "Daniel Alpay and Izchak Lewkowicz",

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AU - Lewkowicz, Izchak

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AB - We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.

KW - Composition

KW - Convex invertible cones

KW - Electrical circuits

KW - Feedback loops

KW - Positive real functions

KW - Rational functions of non-commuting variables

KW - State-space realization

KW - Stieltjes functions

UR - http://www.scopus.com/inward/record.url?scp=85068378107&partnerID=8YFLogxK

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M3 - Article

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SN - 0024-3795

VL - 580

SP - 359

EP - 383

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Composition of rational functions: State-space realization and applications

Abstract

Keywords

ASJC Scopus subject areas

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