Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

J.A. Ball; S. ter Horst

doi:10.1007/978-3-0346-0161-0_2

Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

J.A. Ball
, S. ter Horst

extern

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

Abstract

The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in $H^\infty$-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional systems, while Nevanlinna-Pick interpolation theory has moved on independently to a variety of multivariable settings. Here we review these developments and indicate the precise connections which survive in the more general multidimensional/multivariable incarnations of the two theories

Original language	English
Title of host publication	Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday
Editors	J.A. Ball
Place of Publication	Basel
Publisher	Birkhäuser
Pages	13-88
Number of pages	66
DOIs	https://doi.org/10.1007/978-3-0346-0161-0_2
Publication status	Published - 2010

Bibliographical note

International Workshop on Operator Theory and its Applications

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10.1007/978-3-0346-0161-0_2

Cite this

Ball, J. A., & ter Horst, S. (2010). Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation. In J. A. Ball (Ed.), Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday (pp. 13-88). Birkhäuser. https://doi.org/10.1007/978-3-0346-0161-0_2

Ball, J.A. ; ter Horst, S. / Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation. Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday. editor / J.A. Ball. Basel : Birkhäuser, 2010. pp. 13-88

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abstract = "The connection between the standard \$H\textasciicircum{}\textbackslash{}infty\$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in \$H\textasciicircum{}\textbackslash{}infty\$-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional systems, while Nevanlinna-Pick interpolation theory has moved on independently to a variety of multivariable settings. Here we review these developments and indicate the precise connections which survive in the more general multidimensional/multivariable incarnations of the two theories",

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Ball, JA & ter Horst, S 2010, Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation. in JA Ball (ed.), Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday. Birkhäuser, Basel, pp. 13-88. https://doi.org/10.1007/978-3-0346-0161-0_2

Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation. / Ball, J.A.; ter Horst, S.
Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday. ed. / J.A. Ball. Basel: Birkhäuser, 2010. p. 13-88.

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

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N2 - The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in $H^\infty$-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional systems, while Nevanlinna-Pick interpolation theory has moved on independently to a variety of multivariable settings. Here we review these developments and indicate the precise connections which survive in the more general multidimensional/multivariable incarnations of the two theories

AB - The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in $H^\infty$-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional systems, while Nevanlinna-Pick interpolation theory has moved on independently to a variety of multivariable settings. Here we review these developments and indicate the precise connections which survive in the more general multidimensional/multivariable incarnations of the two theories

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DO - 10.1007/978-3-0346-0161-0_2

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BT - Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday

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Ball JA, ter Horst S. Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation. In Ball JA, editor, Topics in operator theory : proceedings of the XIXth International Workshop on Operator Theory and its Applications, College of William and Mary, 2008 : a tribute to Israel Gohberg on the occasion of his 80th birthday. Basel: Birkhäuser. 2010. p. 13-88 doi: 10.1007/978-3-0346-0161-0_2

Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

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Bibliographical note

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