Geodesic
Exponential stability of solutions to nonlinear time-delay systems of neutral type
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34K20
Keywords: time-delay systems, neutral equation, exponential stability, attraction sets 
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     author = {Demidenko, Gennadii V. and Matveeva, Inessa I.},
     title = {Exponential stability of solutions to nonlinear time-delay systems of neutral type},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a47/}
}
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Demidenko, Gennadii V.; Matveeva, Inessa I. Exponential stability of solutions to nonlinear time-delay systems of neutral type. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a47/