Electron. J. Diff. Equ., Vol. 2015 (2015), No. 34, pp. 1-14.

Estimates for solutions to a class of nonlinear time-delay systems of neutral type

Gennadii V. Demidenko, Inessa I. Matveeva

Abstract:
We consider nonlinear time-delay systems of neutral type with constant coefficients in the linear terms,
$$ \frac{d}{dt}\big(y(t) + D y(t-\tau)\big) = A y(t) + B y(t-\tau) + F(t, y(t), y(t-\tau)). $$
We obtain estimates characterizing the exponential decay of solutions at infinity, and dependending on the norms of the powers of D.

Submitted November 3, 2014. Published February 6, 2015.
Math Subject Classifications: 34K20.
Key Words: Time-delay systems; neutral type; exponential stability; Lyapunov-Krasovskii functional.

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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

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