From h.kwakernaak@math.utwente.nl Wed Feb 18 07:59:55 1998 Return-Path: Delivered-To: skoge@chembio.ntnu.no Received: (qmail 5821 invoked from network); 18 Feb 1998 07:59:54 -0000 Received: from utmfu6.math.utwente.nl (130.89.60.46) by senja.chembio.ntnu.no with SMTP; 18 Feb 1998 07:59:54 -0000 Received: from math.utwente.nl (utmsu6.math.utwente.nl) by utmfu6.math.utwente.nl with ESMTP (1.40.112.8/16.2) id AA076918792; Wed, 18 Feb 1998 08:59:52 +0100 Sender: H.Kwakernaak@math.utwente.nl Message-Id: <34EA94F7.8DF3572E@math.utwente.nl> Date: Wed, 18 Feb 1998 08:59:51 +0100 From: Huibert Kwakernaak Organization: University of Twente X-Mailer: Mozilla 4.04 [en] (X11; I; HP-UX B.10.10 9000/715) Mime-Version: 1.0 To: Sigurd Skogestad Subject: My Talk Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: R Content-Length: 2084 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 H.Kwakernaak@math.utwente.nl WWW http://www.math.utwente.nl/sb ===================================