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Cheap compensation in disturbed linear dynamical systems with multi-input delays

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Abstract

In this paper, we investigate the remediability problem of any disturbances for a class of distributed systems with multiple input delays. We show how to remedy any disturbance effect with a convenient choice of the control operator through the observation. The developments are based on semigroups theory and using an extension of Hilbert Uniqueness Method. An application to hyperbolic systems is presented. The usual case of sensors and actuators is examined and numerical simulations are also given.

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Notes

  1. This problem can be also considered as compensation one, without risk of confusion with other related notions such that of compensator which concerns the asymptotic reconstruction of the state of the system.

  2. This means that the actuator is active only in D. Its spatial distribution g is considered as null on out of the geometrical support D.

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Authors and Affiliations

  1. Faculty of Sciences Ain Chock, University Hassan II, B.P. 5366, Maârif, Casablanca, Morocco

    Salma Souhaile & Larbi Afifi

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  1. Salma Souhaile
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  2. Larbi Afifi
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Correspondence to Salma Souhaile.

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Souhaile, S., Afifi, L. Cheap compensation in disturbed linear dynamical systems with multi-input delays. Int. J. Dynam. Control 8, 243–253 (2020). https://doi.org/10.1007/s40435-018-00505-6

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  • DOI: https://doi.org/10.1007/s40435-018-00505-6

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