ar X iv : 0 90 6 . 33 63 v 1 [ m at h . O C ] 1 8 Ju n 20 09 ROBUST CONTROL , MULTIDIMENSIONAL SYSTEMS AND MULTIVARIABLE NEVANLINNA - PICK INTERPOLATION

The connection between the standard H ∞-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 ∞-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.