Journal Article

Feedback theory for time-varying regular linear systems with input and state delays

Said Hadd, Abdelaziz Rhandi and Roland Schnaubelt

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 1, pages 85-110
Published in print March 2008 | ISSN: 0265-0754
Published online March 2007 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnm011
Feedback theory for time-varying regular linear systems with input and state delays

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We show that the class of regular time-varying systems is invariant under perturbations by time-varying state and input delays. In particular, we give explicit formulas of the resulting input, output and input–output maps. This result is used to solve the feedback problem for the delayed system. The relationship between the open- and the closed-loop system is investigated. Our results are applied to a parabolic boundary control problem with input and state delays.

Keywords: regular time-varying systems; retarded evolution equation; input delay; Lebesgue extension; feedback

Journal Article.  0 words. 

Subjects: Mathematics

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