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.