Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

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Ball, J. A.
ter Horst, S.
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Abstract
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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.
Comment: 66 pages
Keywords
Mathematics - Optimization and Control, Mathematics - Functional Analysis, 47A57, 93D09, 13F25, 47A56, 47A63, 93B52, 93D15
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