Geodesic
On the stability of tubes of discontinuous solutions of bilinear systems with delay
The Bulletin of Irkutsk State University. Series Mathematics, Tome 31 (2020), pp. 96-110

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The paper considers the stability property of tubes of discontinuous solutions of a bilinear system with a generalized action on the right-hand side and delay. A feature of the system under consideration is that a generalized (impulsive) effect is possible non-unique reaction of the system. As a result, the unique generalized action gives rise to a certain set of discontinuous solutions, which in the work will be called the tube of discontinuous solutions.The concept of stability of discontinuous solutions tubes is formalized. Two versions of sufficient conditions for asymptotic stability are obtained. In the first case, the stability of the system is ensured by the stability property of a homogeneous system without delay; in the second case, the stability property is ensured by the stability property of a homogeneous system with delay. These results generalized the similar results for systems without delay.
Keywords: differential equations with delay, impulsive disturbance, stability. 
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     author = {A. N. Sesekin and N. I. Zhelonkina},
     title = {On the stability of tubes of discontinuous solutions of bilinear systems with delay},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a6/}
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A. N. Sesekin; N. I. Zhelonkina. On the stability of tubes of discontinuous solutions of bilinear systems with delay. The Bulletin of Irkutsk State University. Series Mathematics, Tome 31 (2020), pp. 96-110. http://geodesic.mathdoc.fr/item/IIGUM_2020_31_a6/