Geodesic
The stability of differential-difference systems with linearly increasing delay. II.~Systems with additive right side
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 4-9

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The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.
Keywords: system of linear differential-differencel equations, linearly increasing, time delay, asymptotic stability, homogeneous system. 
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     author = {A. V. Ekimov and A. P. Zhabko and P. V. Yakovlev},
     title = {The stability of differential-difference systems with linearly increasing delay. {II.~Systems} with additive right side},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a0/}
}
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A. V. Ekimov; A. P. Zhabko; P. V. Yakovlev. The stability of differential-difference systems with linearly increasing delay. II.~Systems with additive right side. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 4-9. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a0/