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Published May 2002 | Published
Book Section - Chapter Open

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


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.

Additional Information

© 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.

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