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

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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/}
}
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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/