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IMA Journal of Mathematical Control and Information Advance Access originally published online on March 14, 2007
IMA Journal of Mathematical Control and Information 2008 25(1):85-110; doi:10.1093/imamci/dnm011
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Said Hadd{dagger} and Abdelaziz Rhandi{ddagger}

Department of Mathematics, University Cadi Ayyad, Faculty of Sciences, B.P. 2390, 40000 Marrakesh, Morocco

Roland Schnaubelt§

Department of Mathematics, University of Karlsruhe, 76128 Karlsruhe, Germany

{dagger} Email: hadd{at}ucam.ac.ma

{ddagger} Email: rhandi{at}ucam.ac.ma

§ Corresponding author. Email: schnaubelt{at}math.uni-karlsruhe.de

Received on January 23, 2006; Accepted on November 17, 2006

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.


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