Electron. J. Diff. Equ., Vol. 2016 (2016), No. 19, pp. 1-20.

Exponential stability of solutions to nonlinear time-delay systems of neutral type

Gennadii V. Demidenko, Inessa I. Matveeva

Abstract:
We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms
$$ \frac{d}{dt}\big(y(t) + D y(t-\tau)\big) = A y(t) + B y(t-\tau) + F(t, y(t), y(t-\tau)), $$
where
$$ \|F(t,u,v)\| \le q_1\|u\|^{1+\omega_1} + q_2\|v\|^{1+\omega_2}, \quad q_1, q_2, \omega_1, \omega_2 > 0. $$
We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution.

Submitted October 6, 2015. Published January 11, 2016.
Math Subject Classifications: 34K20.
Key Words: Time-delay systems; neutral equation; exponential stability; attraction sets.

Show me the PDF file (298 KB), TEX file for this article.

Gennadii V. Demidenko
Laboratory of Differential and Difference Equations
Sobolev Institute of Mathematics
4, Acad. Koptyug avenue, Novosibirsk 630090, Russia
email: demidenk@math.nsc.ru
Inessa I. Matveeva
Laboratory of Differential and Difference Equations
Sobolev Institute of Mathematics
4, Acad. Koptyug avenue, Novosibirsk 630090, Russia
email: matveeva@math.nsc.ru

Return to the EJDE web page