  This paper focuses on using the first curvature $\kappa(t)$ of trajectory to
describe the stability of linear time-invariant system. We extend the results
for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al.,
arXiv:1808.00290] to $n$-dimensional systems. We prove that for a system
$\dot{r}(t)=Ar(t)$, (i) if there exists a measurable set whose Lebesgue measure
is greater than zero, such that for all initial values in this set,
$\lim\limits_{t\to+\infty}\kappa(t)\neq0$ or
$\lim\limits_{t\to+\infty}\kappa(t)$ does not exist, then the zero solution of
the system is stable; (ii) if the matrix $A$ is invertible, and there exists a
measurable set whose Lebesgue measure is greater than zero, such that for all
initial values in this set, $\lim\limits_{t\to+\infty}\kappa(t)=+\infty$, then
the zero solution of the system is asymptotically stable.
