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IMA Journal of Mathematical Control and Information Advance Access originally published online on July 12, 2005
IMA Journal of Mathematical Control and Information 2005 22(4):423-439; doi:10.1093/imamci/dni035
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Said Hadd** and Abdelali Idrissi***

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

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

*** Email: idrissi{at}ucam.ac.ma

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.

Received on 7 June 2004. accepted on 5 January 2005.


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