Properties of the realization of inner functions

Birgit Jacob; Hans Zwart

Properties of the realization of inner functions

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In this paper we investigate state-space realizations of inner functions. We derive necessary and sufficient, conditions on basis of the inner function to have a exactly controllable and exactly observable realization such that the associated C₀-semigroup is exponentially stable. Furthermore. we give necessary and sufficient conditions on the inner function such that the C₀-semigroup is a group. Combining these results, the C₀-semigroup is an exponentially stable C₀- group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.

Original language	English
Title of host publication	European Control Conference, ECC 1999 - Conference Proceedings
Publisher	IEEE
Pages	3411-3414
Number of pages	4
ISBN (Electronic)	9783952417355
Publication status	Published - 24 Mar 2015
Event	1999 European Control Conference, ECC 1999 - Karlsruhe, Germany Duration: 31 Aug 1999 → 3 Sept 1999

Conference

Conference	1999 European Control Conference, ECC 1999
Abbreviated title	ECC
Country/Territory	Germany
City	Karlsruhe
Period	31/08/99 → 3/09/99

Keywords

exactly controllable and exactly observable realization
exponential stability
inner function
Realization theory

Cite this

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title = "Properties of the realization of inner functions",

abstract = "In this paper we investigate state-space realizations of inner functions. We derive necessary and sufficient, conditions on basis of the inner function to have a exactly controllable and exactly observable realization such that the associated C0-semigroup is exponentially stable. Furthermore. we give necessary and sufficient conditions on the inner function such that the C0-semigroup is a group. Combining these results, the C0-semigroup is an exponentially stable C0- group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.",

keywords = "exactly controllable and exactly observable realization, exponential stability, inner function, Realization theory",

author = "Birgit Jacob and Hans Zwart",

year = "2015",

month = mar,

day = "24",

language = "English",

pages = "3411--3414",

booktitle = "European Control Conference, ECC 1999 - Conference Proceedings",

publisher = "IEEE",

address = "United States",

note = "1999 European Control Conference, ECC 1999, ECC ; Conference date: 31-08-1999 Through 03-09-1999",

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TY - GEN

T1 - Properties of the realization of inner functions

AU - Jacob, Birgit

AU - Zwart, Hans

PY - 2015/3/24

Y1 - 2015/3/24

N2 - In this paper we investigate state-space realizations of inner functions. We derive necessary and sufficient, conditions on basis of the inner function to have a exactly controllable and exactly observable realization such that the associated C0-semigroup is exponentially stable. Furthermore. we give necessary and sufficient conditions on the inner function such that the C0-semigroup is a group. Combining these results, the C0-semigroup is an exponentially stable C0- group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.

AB - In this paper we investigate state-space realizations of inner functions. We derive necessary and sufficient, conditions on basis of the inner function to have a exactly controllable and exactly observable realization such that the associated C0-semigroup is exponentially stable. Furthermore. we give necessary and sufficient conditions on the inner function such that the C0-semigroup is a group. Combining these results, the C0-semigroup is an exponentially stable C0- group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.

KW - exactly controllable and exactly observable realization

KW - exponential stability

KW - inner function

KW - Realization theory

UR - http://www.scopus.com/inward/record.url?scp=84930609190&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84930609190

SP - 3411

EP - 3414

BT - European Control Conference, ECC 1999 - Conference Proceedings

PB - IEEE

T2 - 1999 European Control Conference, ECC 1999

Y2 - 31 August 1999 through 3 September 1999

ER -

Properties of the realization of inner functions

Abstract

Conference

Keywords

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