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Simultaneous Stabilization of a Family of Delay Differential Systems by a Dynamic State Feedback

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Abstract

For a spectrally controllable linear autonomous system with commensurate delays, a dynamic state feedback is constructed in the form of a differential–difference controller that provides the closed-loop system with finite-time stabilization (complete damping of the original system in finite time). This problem is solved by reducing the original system to a system with finite spectrum (spectral reduction) by an inner controller loop determined by some vector polynomial. Then the outer loop of the controller is constructed that provides the closed-loop system with finite-time stabilization. Conditions on the coefficients of the family of spectrally controllable linear autonomous systems of the same order with the same commensurate delays are specified under which the specified controller will be the same for all systems in the family, thereby solving the problem of simultaneous finite-time stabilization of such a family.The results are illustrated by examples.

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Authors and Affiliations

  1. Belarusian National Technical University, Minsk, 220013, Belarus

    A. V. Metel’skii

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  1. A. V. Metel’skii
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Correspondence to A. V. Metel’skii.

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Translated by V. Potapchouck

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Metel’skii, A.V. Simultaneous Stabilization of a Family of Delay Differential Systems by a Dynamic State Feedback. Diff Equat 57, 1495–1515 (2021). https://doi.org/10.1134/S0012266121110094

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