### Optimization and Systems Theory Seminar

Friday, April 23, 1999, 11.00-12.00, Room 3721, Lindstedtsvägen 25

** Professor Danny C. Sorensen **

Rice University

Houston, Texas, USA

E-mail:
sorensen@caam.rice.edu

(Visiting professor at KTH during the spring of 1999.)

####
Krylov projection methods for model reduction

This talk will survey some numerical techniques for obtaining reduced
order models of large state space systems of the form x' = Ax + Bu, y =
Cx, where A,B,C are n by n, n by m and m by n matrices, and x,y,u are
vector functions of time with dimensions n,m and m. Such systems
arise in the analysis of large linear circuits and also through
discretization of control systems involving time dependent partial
differential equations.
Computational cost motivates the development of reduced order models
which accurately approximate the response y of the full system for a
given input u. We shall survey various Krylov subspace projection
techniques and discuss connections between the Lanczos algorithm and
classic moment theory. We shall also discuss approches to obtaining
partial balanced realizations (or reduced models). This approach has
the potential to provide two important features that are usually
lacking in existing model reduction schemes.

Rigorous bounds on the H-infinity norm of the difference between the
full order system and the reduced order system in terms of the Hankel
singular values neglected by the reduced order system.

Straightforward extension from single input single output (SISO) to to
multiple input multiple output (MIMO) systems.

Calendar of seminars

*Last update: April 21, 1999 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*