Stability of solutions to differential equations of neutral type

G. V. Demidenko   ; T. V. Kotova   ; M. A. Skvortsova

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 17-29

Résumé

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.

Détail

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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