Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations

Gennadii V. Demidenko and Inessa I. Matveeva
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Gennadii V. Demidenko: Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
Inessa I. Matveeva: Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, Russia

Mathematics, 2021, vol. 9, issue 16, 1-13

Abstract: We consider a class of second-order nonlinear delay differential equations with periodic coefficients in linear terms. We obtain conditions under which the zero solution is asymptotically stable. Estimates for attraction sets and decay rates of solutions at infinity are established. This class of equations includes the equation of vibrations of the inverted pendulum, the suspension point of which performs arbitrary periodic oscillations along the vertical line.

Keywords: delay differential equations; periodic coefficients; inverted pendulum; asymptotic stability; Lyapunov differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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