State space theory of automorphisms of rational matrix functions

Daniel Alpay; Joseph A. Ball; Israel Gohberg; Leiba Rodman

doi:10.1007/BF01200324

State space theory of automorphisms of rational matrix functions

Daniel Alpay, Joseph A. Ball, Israel Gohberg, Leiba Rodman

Department of Mathematics

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

10 Scopus citations

Abstract

The state space theory from linear control theory is used as a tool to describe the action of automorphisms of a certain form acting on rational matrix functions. This class consists of automorphisms representable as the composition of a linear fractional change of variable together with the operations of inverse-transpose, conjugation and an inner automorphism. We also describe in state space terms minimal factorizations within the class of functions of a certain associated group.

Original language	English
Pages (from-to)	349-377
Number of pages	29
Journal	Integral Equations and Operator Theory
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/BF01200324
State	Published - 1 May 1992

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01200324

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title = "State space theory of automorphisms of rational matrix functions",

abstract = "The state space theory from linear control theory is used as a tool to describe the action of automorphisms of a certain form acting on rational matrix functions. This class consists of automorphisms representable as the composition of a linear fractional change of variable together with the operations of inverse-transpose, conjugation and an inner automorphism. We also describe in state space terms minimal factorizations within the class of functions of a certain associated group.",

author = "Daniel Alpay and Ball, \{Joseph A.\} and Israel Gohberg and Leiba Rodman",

year = "1992",

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AU - Alpay, Daniel

AU - Ball, Joseph A.

AU - Gohberg, Israel

AU - Rodman, Leiba

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N2 - The state space theory from linear control theory is used as a tool to describe the action of automorphisms of a certain form acting on rational matrix functions. This class consists of automorphisms representable as the composition of a linear fractional change of variable together with the operations of inverse-transpose, conjugation and an inner automorphism. We also describe in state space terms minimal factorizations within the class of functions of a certain associated group.

AB - The state space theory from linear control theory is used as a tool to describe the action of automorphisms of a certain form acting on rational matrix functions. This class consists of automorphisms representable as the composition of a linear fractional change of variable together with the operations of inverse-transpose, conjugation and an inner automorphism. We also describe in state space terms minimal factorizations within the class of functions of a certain associated group.

UR - https://www.scopus.com/pages/publications/30244489310

U2 - 10.1007/BF01200324

DO - 10.1007/BF01200324

M3 - Article

AN - SCOPUS:30244489310

SN - 0378-620X

VL - 15

SP - 349

EP - 377

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

State space theory of automorphisms of rational matrix functions

Abstract

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