M. Ashordia, N. Kekelia

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

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 $\lim\limits_{t\to +\infty} \xi(t)=+\infty$