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IMA Journal of Mathematical Control and Information Advance Access published online on July 12, 2005
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dni035
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IMA Journal of Mathematical Control and Information © Institute of Mathematics and its Applications 2005; all rights reserved.
Received June 7, 2004
Accepted January 5, 2005

Article

Regular linear systems governed by systems with state, input and output delays

Said Hadd 1* and Abdelali Idrissi 1

1 Department of Mathematics, Faculty of Sciences Semlalia, University Cadi Ayyad, BP 2390, 40000 Marrakesh, Morocco

* To whom correspondence should be addressed.
Said Hadd, E-mail: hadd{at}ucam.ac.ma


  Abstract

In this paper, we give a new reformulation of linear systems with delays in input, state and output. We show that these systems can be written as a regular linear system without delays. The technique used here is essentially based on the theory recently developed by Salamon and Weiss and the shift in semigroup properties. Our framework can be applied, in particular, when the delay operators are given by Riemann-Stieltjes integrals.

Keywords: infinite-dimensional linear systems; delay operators; regular linear systems; Banach space.
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