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A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

Sznaier, M. and Doherty, A. C. and Barahona, M. and Mabuchi, H. and Doyle, J. C. (2002) A new bound of the ℒ2[0, T]-induced norm and applications to model reduction. In: American Control Conference 2002, Anchorage, Alaska, 8-10 May 2002. Vol.2. IEEE , Piscataway, NJ, pp. 1180-1185. ISBN 0-7803-7298-0 http://resolver.caltech.edu/CaltechAUTHORS:SZNacc02

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Abstract

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics.


Item Type:Book Section
Additional Information:© Copyright 2002 IEEE. Reprinted with permission. The authors are indebted to Pablo Parrilo, Aristo Asimakopoulos, Henrik Sandberg and Alexandre Megretski for discussions on model reduction of unstable systems and its application to problems in classical physics. This work was supported in part by NSF, under grants ECS-9907051, ECS-0115946 and Caltech’s Institute for Quantum Information, and by AFOSR, under MURI “Uncertainty Management in Complex Systems” and grant F49620-00-1-0020.
Subject Keywords:linear systems, matrix algebra, reduced order systems
Record Number:CaltechAUTHORS:SZNacc02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SZNacc02
Alternative URL:http://dx.doi.org/10.1109/ACC.2002.1023179
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8686
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:05 Sep 2007
Last Modified:26 Dec 2012 09:41

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