Geodesic
Estimates for solutions to a class of nonlinear time-delay systems of neutral type
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 34K20
Keywords: time-delay systems, neutral type, exponential stability, Lyapunov-Krasovskiĭ functional 
@article{EJDE_2015__2015__a5,
     author = {Demidenko,  Gennadii V. and Matveeva,  Inessa I.},
     title = {Estimates for solutions to a class of nonlinear time-delay systems of neutral type},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1312.34110},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a5/}
}
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Demidenko,  Gennadii V.; Matveeva,  Inessa I. Estimates for solutions to a class of nonlinear time-delay systems of neutral type. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a5/