A realization theorem for rational functions of several complex variables

D. Alpay; C. Dubi

doi:10.1016/S0167-6911(02)00326-2

A realization theorem for rational functions of several complex variables

D. Alpay, C. Dubi

Department of Mathematics

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

32 Scopus citations

Abstract

Proof for a realization theorem for rational functions of several complex variables was presented. The theorem states that a matrix-valued rational function F(z) analytic in a neighbourhood of the origin can be written as: F(z) = D + C(I_n - zA)^-1zB, where D = F(0) and A, B and C are matrices of appropriate sizes. This representation allows to consider F as the transfer function of a linear system.

Original language	English
Pages (from-to)	225-229
Number of pages	5
Journal	Systems and Control Letters
Volume	49
Issue number	3
DOIs	https://doi.org/10.1016/S0167-6911(02)00326-2
State	Published - 5 Jul 2003

Keywords

Multi-indexed systems
Realization theory

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science (all)
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/S0167-6911(02)00326-2

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abstract = "Proof for a realization theorem for rational functions of several complex variables was presented. The theorem states that a matrix-valued rational function F(z) analytic in a neighbourhood of the origin can be written as: F(z) = D + C(In - zA)-1zB, where D = F(0) and A, B and C are matrices of appropriate sizes. This representation allows to consider F as the transfer function of a linear system.",

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AB - Proof for a realization theorem for rational functions of several complex variables was presented. The theorem states that a matrix-valued rational function F(z) analytic in a neighbourhood of the origin can be written as: F(z) = D + C(In - zA)-1zB, where D = F(0) and A, B and C are matrices of appropriate sizes. This representation allows to consider F as the transfer function of a linear system.

KW - Multi-indexed systems

KW - Realization theory

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JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

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ER -

A realization theorem for rational functions of several complex variables

Abstract

Keywords

ASJC Scopus subject areas

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