State Space Formulas for a Solution of the Suboptimal Nehari Problem on the Unit Disc

Ruth F. Curtain; Mark R. Opmeer

doi:10.1007/s00020-009-1679-9

State Space Formulas for a Solution of the Suboptimal Nehari Problem on the Unit Disc

Ruth F. Curtain
, Mark R. Opmeer^*

^*Corresponding author voor dit werk

Onderzoeksoutput › Academic › peer review

1 Citaat (Scopus)

Samenvatting

We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability, we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve the problem for general H-infinity functions.

Originele taal-2	English
Pagina's (van-tot)	35-59
Aantal pagina's	25
Tijdschrift	Integral equations and operator theory
Volume	64
Nummer van het tijdschrift	1
DOI's	https://doi.org/10.1007/s00020-009-1679-9
Status	Published - mei-2009

Toegang tot document

10.1007/s00020-009-1679-9

Handle.net

Permanente koppeling

Document onder embargo

State Space Formulas for a Solution of the Suboptimal Nehari Problem
Final publisher's version, 298 KB
Kopie aanvragen

Citeer dit

@article{39fd3754bacd4e83b8ee96e360dc8bf1,

title = "State Space Formulas for a Solution of the Suboptimal Nehari Problem on the Unit Disc",

abstract = "We give state space formulas for a ({"}central{"}) solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability, we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve the problem for general H-infinity functions.",

keywords = "Infinite-dimensional linear systems, J-spectral factorizations, Hankel operators, Lyapunov equations, Nehari problem, INFINITE-DIMENSIONAL SYSTEMS, LINEAR-SYSTEMS",

author = "Curtain, \{Ruth F.\} and Opmeer, \{Mark R.\}",

year = "2009",

month = may,

doi = "10.1007/s00020-009-1679-9",

language = "English",

volume = "64",

pages = "35--59",

journal = "Integral equations and operator theory",

issn = "0378-620X",

publisher = "SPRINGER BASEL AG",

number = "1",

}

TY - JOUR

T1 - State Space Formulas for a Solution of the Suboptimal Nehari Problem on the Unit Disc

AU - Curtain, Ruth F.

AU - Opmeer, Mark R.

PY - 2009/5

Y1 - 2009/5

N2 - We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability, we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve the problem for general H-infinity functions.

AB - We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability, we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve the problem for general H-infinity functions.

KW - Infinite-dimensional linear systems

KW - J-spectral factorizations

KW - Hankel operators

KW - Lyapunov equations

KW - Nehari problem

KW - INFINITE-DIMENSIONAL SYSTEMS

KW - LINEAR-SYSTEMS

U2 - 10.1007/s00020-009-1679-9

DO - 10.1007/s00020-009-1679-9

M3 - Article

SN - 0378-620X

VL - 64

SP - 35

EP - 59

JO - Integral equations and operator theory

JF - Integral equations and operator theory

IS - 1

ER -

State Space Formulas for a Solution of the Suboptimal Nehari Problem on the Unit Disc

Samenvatting

Toegang tot document

Handle.net

Document onder embargo

Vingerafdruk

Citeer dit