EECS Joint Colloquium Distinguished Lecture Series
     
 

Wednesday, October 16, 2002
Hewlett Packard Auditorium, 306 Soda Hall
4:00-5:00 p.m.

Professor Anders Lindquist

Division of Optimization and Systems Theory,
Department of Mathematics, Royal Institute of Technology

 
 

Analytic Interpolation With Degree Constraint and Applications to Systems, Control and Signal Processing

 

Abstract:

   

Many important problems in circuit theory, robust stabilization and control, signal processing, speech synthesis, and stochastic systems theory can be formulated as analytic interpolation problems. For these problems the (real) interpolants are (i) positive real, i.e., analytic in the unit disc (or its complement) and mapping it into the closed left-half plane, and (ii) rational of a prescribed maximal degree. Removing the degree requirement (ii), this is a classical problem going back to Schur, Carath{\'e}odory, Toeplitz, Nevanlinna and Pick. However, the degree constraint is essential in applications, and it considerably alters the mathematical problem. In fact, if there are $n+1$ interpolation points, there is a complete parameterization of all interpolants of degree at most $n$ in terms of spectral zeros, which hence become design parameters. Each such solution can be determined by solving a convex optimization problem.

In this talk we show how these ideas can be applied to problems in spectral estimation and robust control. In the control applications we take a global analysis approach where we consider bijective transformations from spaces of tuning parameters to entire classes of controllers.

    Biography:
   

Anders Lindquist received his PhD degree from the Royal Institute of Technology, Stockholm, Sweden, where in 1972 he was appointed a Docent of Optimization and Systems Theory. From 1972 to 1974 he held visiting positions at the University of Florida, Brown University, and State University of New York at Albany. In 1974 he became an Associate Professor, and in 1980 a (full) Professor of Mathematics at the University of Kentucky,where he remained until 1983. He is now a Professor at the Royal Institute of Technology, where in 1982 he was appointed to the Chair of Optimization and Systems Theory. Since then he has also held visiting positions at the University of Padova, Italy, University of Arizona, USSR Academy of Sciences, Moscow, East China Normal University, Shanghai, and Technion, Haifa, Israel.

Presently, Anders Lindquist is the Chairman of the Mathematics Department at the Royal Institute of Technology. He is a Member of the Royal Swedish Academy of Engineering Sciences, a Foreign Member of the Russian Academy of Natural Sciences, a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), and an Honorary Member the Hungarian Operations Research Society. He is an Affiliate Professor at Washington University, St Louis (since 1989) and an Advisory Board Member of the Institute for Mathematics of the Life Sciences, Texas Tech University.

Lindquist has served on many editorial boards of journals, among them the Journal of Mathematical Systems, Estimation, and Control (Communicating Editor), Systems and Control Letters, Adaptive Control and Signal Processing, and book series, namely Systems and Control: Foundations and Applications, Applied and Computational Control, Signals, and Circuits, and Progress in Systems and Control. Since 1983 he has been a member, and between 1985 and 1987 the chairman, of the steering committee for the biennial international symposia on the MathematicalTheory of Networks and Systems (MTNS).