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Instability of systems with linear delay reducible to singularly perturbed ones

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Abstract

We investigate the stability of linear systems of linear delay differential equations in the case when one of subsystems is singular. We establish sufficient conditions for the instability of solutions to such systems. We solve the considered problem with the help of the Laplace transformation.

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References

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Authors and Affiliations

  1. Ural State University, pr. Lenina 51, Ekaterinburg, 620083, Russia

    B. G. Grebenshchikov

  2. Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, ul. S. Kovalevskoi 16, Ekaterinburg, 620219, Russia

    S. I. Novikov

Authors
  1. B. G. Grebenshchikov
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  2. S. I. Novikov
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Corresponding author

Correspondence to S. I. Novikov.

Additional information

Original Russian Text © B.G. Grebenshchikov and S.I. Novikov, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 2, pp. 3–13.

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Grebenshchikov, B.G., Novikov, S.I. Instability of systems with linear delay reducible to singularly perturbed ones. Russ Math. 54, 1–10 (2010). https://doi.org/10.3103/S1066369X10020015

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  • DOI: https://doi.org/10.3103/S1066369X10020015

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