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The Regular Linear Systems Associated with the Shift Semigroups and Application to Control Linear Systems with Delay

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Abstract

We investigate the infinite dimensional control linear systems with delays in the state and input. We give a new variation of constants formula when the state and control delay operators are unbounded. We prove the existence of mild and classical solutions of such systems. Our approach is based on the theory of abstract and regular linear systems introduced by Salamon (Math Syst Theor 21:147–164, 1989) and Weiss (Isr J Math 65:17–43, 1989). Finally, we apply our abstract framework to an example from population dynamics.

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Authors and Affiliations

  1. Faculty of Science Semlalia, Department of Mathematics, Cadi Ayyad University, B.P. 2390, 40000, Marrakesh, Morocco

    S. Hadd, A. Idrissi & A. Rhandi

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  1. S. Hadd
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  2. A. Idrissi
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  3. A. Rhandi
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Correspondence to A. Rhandi.

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Hadd, S., Idrissi, A. & Rhandi, A. The Regular Linear Systems Associated with the Shift Semigroups and Application to Control Linear Systems with Delay. Math. Control Signals Syst. 18, 272–291 (2006). https://doi.org/10.1007/s00498-006-0002-4

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  • DOI: https://doi.org/10.1007/s00498-006-0002-4

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