Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

J.A. Ball, S. ter Horst

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-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 languageEnglish
Title of host publicationTopics 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
EditorsJ.A. Ball
Place of PublicationBasel
PublisherBirkhäuser
Pages13-88
Number of pages66
DOIs
Publication statusPublished - 2010

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