**M. Ashordia, N. Kekelia**

## On the **x**-Exponentially Asymptotic Stability of Linear Systems of Generalized Ordinary Differential Equations

**abstract:**

Necessary and sufficient conditions and effective sufficient
conditions are established for the so-called $\xi$-exponentially asymptotic
stability of the linear system
$$ dx(t)=dA(t)\cdot x(t)+df(t), $$
where $A: [0,+\infty[\,\to \bR^{n\times n}$ and $f: [0,+\infty[\,\to \bR^n$
are respectively matrix- and vector-functions with bounded variation components,
on every closed interval from $[0,+\infty[$ and
$\xi: [0,+\infty[\,\to [0,+\infty[$ is a nondecreasing function
such that $\lim\limits_{t\to +\infty} \xi(t)=+\infty$