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The asymptotic stability of a nonstationary system with delay


In this paper we study the exponential stability of a linear system of differential equations with a constant delay such that the right-hand side of one of its subsystems contains an exponential multiplier. We establish sufficient conditions for the existence of an asymptotically periodic solution to the inhomogeneous system.

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Correspondence to B. G. Grebenshchikov.

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Original Russian Text © B.G. Grebenshchikov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 8, pp. 24–33.

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Grebenshchikov, B.G. The asymptotic stability of a nonstationary system with delay. Russ Math. 57, 20–28 (2013).

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Keywords and phrases

  • asymptotic stability
  • exponential bound
  • asymptotically periodic solution