Geodesic
Stability of solutions to differential equations of neutral type
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 17-29

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In the present paper we study stability of solutions to systems of quasi-linear delay differential equations of neutral type $$ \frac{d}{dt}(y(t) + Dy(t-\tau)) = Ay(t) + By(t-\tau) + F(t,y(t),y(t-\tau)), \quad t > \tau, $$ where $A$, $B$, $D$ are $n \times n$ numerical matrices, $\tau > 0$ is a delay parameter, $F(t,u,v)$ is a real-valued vector-function satisfying Lipschitz condition with respect to $u$ and $F(t,0,0) = 0$. Stability conditions of the zero solution to the systems are obtained, uniform estimates for the solutions on the half-axis $\{t>\tau\}$ are established. In the case of asymptotic stability these estimates give the decay rate of the solutions at infinity.
Keywords: quasi-linear differential equations of neutral type, asymptotic stability, uniform estimates for solutions, modified Lyapunov–Krasovskii functional.
Mots-clés : attraction domain 
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     title = {Stability of solutions to differential equations of neutral type},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a1/}
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G. V. Demidenko; T. V. Kotova; M. A. Skvortsova. Stability of solutions to differential equations of neutral type. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 17-29. http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a1/