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Approximation with the output of linear control systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2007 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 329, no 2, 798-821 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we give a new proof that for controllable and observable linear systems every L-2[0, T] function can be approximated in the L-2[0, T] sense with an output function generated by an L-2[0, T] input function. We also give a new characterization of how continuous functions on [0, T] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.

Place, publisher, year, edition, pages
2007. Vol. 329, no 2, 798-821 p.
Keyword [en]
linear systems, approximation, continuous functions, smoothing splines
URN: urn:nbn:se:kth:diva-16430DOI: 10.1016/j.jmaa.2006.03.032ISI: 000244664700006ScopusID: 2-s2.0-33846588040OAI: diva2:334472
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Jönsson, Ulf T.
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