Abstract
When studying systems with delay, a particular attention is paid to such important property as their stability. In investigation of stability of systems of ODEs by the direct Lyapunov method, quadratic Lyapunov functions are widely used. For a system with delay, we suggest to use as Lyapunov functions some quadratic Lyapunov functions constructed for a system of ODEs and satisfying some restrictions on the first derivative. For such systems we find conditions which make possible to use such quadratic functions as Lyapunov functions.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 10, pp. 15–20.
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Antonovskaya, O.G. Application of Quadratic Lyapunov Functions to Investigation of Stability of Systems with Delay. Russ Math. 63, 13–17 (2019). https://doi.org/10.3103/S1066369X19100025
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DOI: https://doi.org/10.3103/S1066369X19100025