Optimization and Systems Theory Seminar
Friday, May 4, 2001, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Professor Olof Staffans
Department of Mathematics
Åbo Akademi University
Åbo, Finland
E-mail: olof.staffans@abo.fi

Well-posed linear systems

A well-posed linear system is a mathematical object which is used, e.g., in the theory of optimal H_2- and H_infty-control of infinite-dimensional systems. Most linear time-independent distributed parameter systems can be described in this form: internal or boundary control of PDE:s, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literatur for a long time: they are closedly connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foias. The theory has developed independently in many different scools, but recently these different approaches have converged.

We begin the talk by presenting the basic theory of well-posed linear systems. Then we describe how these system are related to the Lax-Phillips scattering theory and the Sz.-Nagy-Foias model theory. Special attention is paid to dissipative, energy-preserving and conservative systems. We finish by describing some recent research related to J-energy-preserving well-posed linar systems which appear in optimal control theory (such as H_2 and H_infinity) and the corresponding Riccati equations.

Calendar of seminars
Last update: April 17, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.