### Optimization and Systems Theory Seminar

Friday, March 31, 2000, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Alessandro Chiuso**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail:
alessandro.chiuso@math.kth.se

####
Geometric subspace identification and stochastic
realization with inputs

In this talk geometric subspace methods for the identification of
linear time invariant systems in the presence of exogenous inputs will
be discussed. These methods may be seen, roughly speaking, as the
translation into algorithms which works on data of ideas from
stochastic realization theory. Therefore geometric stochastic
realization for system with inputs will be discussed and some results
from stochastic realization theory will be extended to this case.
Since in practice only a finite amount of data is available one has to
resort to finite interval realization, which will be discussed in some
detail.
Some common subspace algorithms may become rather ill-conditioned in
some situations, yet there is experimental evidence of poor behaviour
in some situations.
We shall therefore discuss to some extent which situations may lead
to poor behaviour (in particular the link with the input process). We
present a possible remedy which shows better performances in some ill
conditioned cases and show simulation results.

Calendar of seminars

*Last update: March 23, 2000 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*