Geodesic
On the stability of one equation with a discrete retarded argument and a constant concentrated delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 90-94.

Voir la notice de l'article provenant de la source Math-Net.Ru

A functional differential equation with a discrete retarded argument and a constant concentrated delay is considered. The problem of the asymptotic stability of this equation is reduced to the problem of the location of the spectrum of the shift operator. Coefficient sufficient conditions for the asymptotic stability of this equation are obtained. The domain in the parameter space such that these conditions are necessary is obtained.
Keywords: functional differential equations, asymptotic stability, discrete retarded argument, hybrid systems. 
@article{IVM_2023_10_a8,
     author = {M. V. Mulyukov},
     title = {On the stability of one equation with a discrete retarded argument and a constant concentrated delay},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {90--94},
     publisher = {mathdoc},
     number = {10},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_10_a8/}
}
TY  - JOUR
AU  - M. V. Mulyukov
TI  - On the stability of one equation with a discrete retarded argument and a constant concentrated delay
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 90
EP  - 94
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_10_a8/
LA  - ru
ID  - IVM_2023_10_a8
ER  - 
%0 Journal Article
%A M. V. Mulyukov
%T On the stability of one equation with a discrete retarded argument and a constant concentrated delay
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 90-94
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_10_a8/
%G ru
%F IVM_2023_10_a8
M. V. Mulyukov. On the stability of one equation with a discrete retarded argument and a constant concentrated delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 90-94. http://geodesic.mathdoc.fr/item/IVM_2023_10_a8/

[1] Kozlov R.I., Kozlova O.R., “Issledovanie ustoichivosti nelineinykh nepreryvno-diskretnykh modelei ekonomicheskoi dinamiki metodom VFL. I”, Izv. RAN. Teoriya i sistemy upravleniya, 2009, no. 2, 104–113

[2] Fridman E., “Stability of linear descriptor systems with delay: a Lyapunov-based approach”, J. Math. Anal. and Appl., 273:1 (2002), 24–44 | DOI | MR | Zbl

[3] Kozlov R.I., Kozlova O.R., “Issledovanie ustoichivosti nelineinykh nepreryvno-diskretnykh modelei ekonomicheskoi dinamiki metodom VFL. II”, Izv. RAN. Teoriya i sistemy upravleniya, 2009, no. 3, 41–50 | Zbl

[4] De la Sen M., “Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems”, Hindawi Publ. Corporation Fixed Point Theory and Appl., 2009, 826438 | DOI | MR | Zbl

[5] Simonov P.M., “K voprosu ob ustoichivosti sistemy dvukh lineinykh gibridnykh funktsionalno-differentsialnykh sistem s posledeistviem”, Vestn. rossiisk. un-ov. Matem., 25:131 (2020), 299–306 | Zbl

[6] Bravyi E., Maksimov V., Simonov P., “Some Economic Dynamics Problems for Hybrid Models with Aftereffect”, Math., 8:10 (2020)

[7] Ye H., Michel A.N., Hou L., “Stability Theory for Hybrid Dynamical Systems”, IEEE Transactions on automatic control, 43:4 (1998) | MR

[8] Marchenko V.M., Loiseau J.-J., “On the Stability of Hybrid Difference-Differential Systems”, Diff. Equat., 45 (2009), 743–756 | DOI | MR | Zbl

[9] Marchenko V.M., Borkovskaya I.M., “Ustoichivost i stabilizatsiya lineinykh gibridnykh diskretno-nepreryvnykh statsionarnykh sistem”, Tr. BGTU. Fiz.-matem. nauki i informatika, 2012, no. 6, 7–10

[10] Azbelev N.V., Maksimov V.P., Rakhmatullina L.F., Vvedenie v teoriyu funktsionalno–differentsialnykh uravnenii, Nauka, M., 1991 | MR

[11] Mulyukov M.V., “Necessary conditions of the stability of one hybrid system”, Memoirs on Diff. Equat. and Math. Phys., 87 (2022), 111–118 | MR | Zbl

[12] Neimark Yu.I., Ustoichivost linearizovannykh sistem (diskretnykh i raspredelennykh), LKVVIA, L., 1949