Subject: My Talk

From: Huibert Kwakernaak <[email-masked]>
Date: Wed, 18 Feb 1998 08:59:51 +0100

Dear Sigurd,

This is the summary of my talk.

Best,

Huibert

-----------------------------------------------------------

Reliable and fast computation of optimal $H_\infty$
solutions for state and descriptor systems

Huibert Kwakernaak
Systems, Signals and Control Group
University of Twente

Recently, a compact and numerically attractive solution
method has been developed for computing sublevel solutions
of the $H_\infty$ problem for linear descriptor systems. The
algorithm may also be used for state systems. It relies on
the transformation of two para-Hermitian matrix pencils to
triangular form as proposed by Clements. The compensator is
computed in descriptor form.

The singularity that often appears in sublevel solutions 
that are close to the truly optimal solution may be
eliminated 
by a slight but significant modification of the spectral 
factorization that underlies the algorithm. This
modification 
allows precise and reliable computation and characterization 
of all optimal solutions. An equally reliable computational 
method is proposed to cancel the indeterminate common factor 
that typically appears in the optimal compensator.

The algorithm includes a level search that converges 
considerably faster to the optimal solution than the usual 
binary line search.

References:

H. Kwakernaak, "Frequency domain solution of the
$\mathcal{H}_\infty$ problem for descriptor systems."
Workshop on Learning, Control and Hybrid Systems,
January 4--8, 1998, Bangalore, India.

D. J. Clements. Rational spectral factorization using
state-space methods. Systems & Control Letters, vol. 20, 
pp.335--343, 1993.

===================================
Huibert Kwakernaak
Department of Applied Mathematics
University of Twente
P. O. Box 217, 7500 AE Enschede
The Netherlands
----------------------------------
Street address: Drienerlolaan 5
7522 NB Enschede, The Netherlands
----------------------------------
Phone Intl+31-53-4893457
FAX   Intl+31-53-4340733
E-mail [email-masked]
WWW http://www.math.utwente.nl/sb
===================================