Validated numerical computation of the L∞-norm for linear dynamical systems

Authors:
Masaaki Kanno;Malcolm C. Smith
Affiliations:
CREST, Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi-shi, Saitama, 332-0012, Japan;Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom
Venue:
Journal of Symbolic Computation
Year:
2006

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Abstract

This paper develops a validated numerical algorithm to compute the L"~-norm, a norm which plays an important role in modern control. The method reduces the L"~-norm computation problem to real root localization of polynomials and some Sturm chain tests, both of which can be executed in a manner which guarantees accuracy. A computational complexity estimate is also given.