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Stabilization of periodic systems with aftereffect by finite-dimensional approximations

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Abstract

We study the stabilization problem for a linear periodic system of differential equations with aftereffect. Approximating systems are described by differential equations with finite-dimensional Volterra operators. We construct admissible controls in the class of piecewise continuous functions by the feedback principle. We establish a connection between the approximating stabilization problem and that of the optimal stabilization for an autonomous linear system of difference equations.

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Authors and Affiliations

  1. Ural Federal University, ul. Mira 19, Ekaterinburg, 620002, Russia

    Yu. F. Dolgii & E. V. Koshkin

Authors
  1. Yu. F. Dolgii
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  2. E. V. Koshkin
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Correspondence to Yu. F. Dolgii.

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Original Russian Text © Yu.F. Dolgii, E.V. Koshkin, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 1, pp. 29–45.

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Dolgii, Y.F., Koshkin, E.V. Stabilization of periodic systems with aftereffect by finite-dimensional approximations. Russ Math. 59, 24–38 (2015). https://doi.org/10.3103/S1066369X1501003X

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  • DOI: https://doi.org/10.3103/S1066369X1501003X

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