J. Rebenda

Asymptotic Properties of Solutions of Real Two-Dimensional Differential Systems with a Finite Number of Constant Delays

abstract:
this article stability and asymptotic properties of a real two-dimensional system $x'(t)=\mathbf A(t) x(t) + \sum\limits_{j=1}^n \mathbf B_j (t) x (t-r_j) + \mathbf h (t, x(t), x(t-r_1),\dots,x(t-r_n))$ are studied, where $r_1>0,\dots,r_n >0$ are constant delays, $\mathbf A,\mathbf B_1,\dots,\mathbf B_n$ are matrix functions and $\mathbf h$ is a vector function. A generalization of results on stability of a two-dimensional differential system with one constant delay is obtained by using the methods of complexification and
Lyapunov--Krasovski\v{\i} functional and some new types of corollaries are presented. The case $\liminf\limits_{t\to\infty}(|a(t)|-|b(t)|)>0$ is studied.

Mathematics Subject Classification: 34K20

Key words and phrases: Stability, asymptotic behaviour, two-dimensional system with delay