An Interpolation Theoretic Approach to Control
Final rept. 1 Jan 1991-31 Mar 1994
MINNESOTA UNIV MINNEAPOLIS DEPT OF ELECTRICAL ENGINEERING
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Our work has been concerned with the utilization of new interpolation and operator theoretic methods for the study of problems in robust control. We have worked on possible nonlinear generalizations of H infinity optimization theory and investigated corresponding intriguing questions in causality which arise in this context. In regard to our work on mu-synthesis and analysis, as well as the multivariable gain margin problem, we have developed a new type of interpolation method which is not norm-based. This is in contrast to the classical Nevanlinna-Pick theory which is used in H infinity design. This line of research leads to spectral radius and structured interpolation extensions of the Nevanlinna-Pick framework. We have also discovered a new lifting technique for the robust stability analysis of systems with several kinds of structured perturbations. We worked in distributed infinite dimensional H infinity control based on our skew Toeplitz methods. These have been applied to certain benchmark examples, e.g., delay systems that appear in aircraft control, and certain flexible beam problems. We have also been applying new curve evolution methods for problems in visual tracking.
- Numerical Mathematics