Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation
Publication date
2010
Authors
Ball, J.A.
ter Horst, S.
Editors
Ball, J.A.
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Part of book
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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
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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. Birkhäuser, Basel, pp. 13-88. https://doi.org/10.1007/978-3-0346-0161-0_2