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On stable solution of the problem of disturbance reduction in a linear dynamical system

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Abstract

We study the problem of active reduction of the influence of a disturbance on the output of a linear controlled system. The problem is studied on a finite time interval. We consider a system of linear differential equations under the action of an unknown disturbance and a control. The problem consists in constructing an algorithm for forming a control that reduces the disturbance on the basis of inaccurate measurements of a part of phase coordinates of the system. This algorithm should form a feedback control such that the trajectory of the given system influenced by an unknown disturbance tracks the trajectory of the reference system. The latter system is described by the same differential equations but with zero control and disturbance. We present two algorithms for solving this problem. These algorithms are robust with respect to informational noises and computational errors.

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Acknowledgements

The author would like to thank the referee for the careful reviewing and the valuable comments to this paper improving its quality.

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  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya Str., Yekaterinburg, Russia, 620990

    V. Maksimov

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  1. V. Maksimov
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Maksimov, V. On stable solution of the problem of disturbance reduction in a linear dynamical system. Math. Control Signals Syst. 36, 177–211 (2024). https://doi.org/10.1007/s00498-023-00363-4

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