Stability of a second-order differential equation with retarded argument

D. Bainov; A. Domoshnitsky

doi:10.1080/02681119408806173

Stability of a second-order differential equation with retarded argument

D. Bainov
, A. Domoshnitsky

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Effective criteria for exponential stability of second-order linear equations based on the positivity of the Cauchy function are proposed. Bounds of the ‘smallness’ of the deviation of the argument are established under which the equation with retarded argument is still stable if the ordinary differential equation with the same coefficients is stable. Based on the criteria obtained, an applied problem on the regulation of concentration is analyzed.

Original language	English
Pages (from-to)	145-151
Number of pages	7
Journal	Dynamics and Stability of Systems
Volume	9
Issue number	2
DOIs	https://doi.org/10.1080/02681119408806173
State	Published - 1 Jan 1994
Externally published	Yes

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title = "Stability of a second-order differential equation with retarded argument",

abstract = "Effective criteria for exponential stability of second-order linear equations based on the positivity of the Cauchy function are proposed. Bounds of the {\textquoteleft}smallness{\textquoteright} of the deviation of the argument are established under which the equation with retarded argument is still stable if the ordinary differential equation with the same coefficients is stable. Based on the criteria obtained, an applied problem on the regulation of concentration is analyzed.",

author = "D. Bainov and A. Domoshnitsky",

note = "Funding Information: In the present investigation, DB was partially supported by the Bulgarian Ministry of Education and Science under Grant MM-7, and AD by a grant from the Israeli Ministry of Science and the 'Ma-Agara'.",

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AU - Domoshnitsky, A.

N1 - Funding Information: In the present investigation, DB was partially supported by the Bulgarian Ministry of Education and Science under Grant MM-7, and AD by a grant from the Israeli Ministry of Science and the 'Ma-Agara'.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - Effective criteria for exponential stability of second-order linear equations based on the positivity of the Cauchy function are proposed. Bounds of the ‘smallness’ of the deviation of the argument are established under which the equation with retarded argument is still stable if the ordinary differential equation with the same coefficients is stable. Based on the criteria obtained, an applied problem on the regulation of concentration is analyzed.

AB - Effective criteria for exponential stability of second-order linear equations based on the positivity of the Cauchy function are proposed. Bounds of the ‘smallness’ of the deviation of the argument are established under which the equation with retarded argument is still stable if the ordinary differential equation with the same coefficients is stable. Based on the criteria obtained, an applied problem on the regulation of concentration is analyzed.

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JO - Dynamics and Stability of Systems

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ER -

Stability of a second-order differential equation with retarded argument

Abstract

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