### 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.
*