  This paper proposes a new approach to describe the stability of linear
time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a
system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there
exists a measurable set $E_1$ with positive Lebesgue measure, such that
$r(0)\in E_1$ implies that $\lim\limits_{t\to+\infty}\tau(t)\neq0$ or
$\lim\limits_{t\to+\infty}\tau(t)$ does not exist, then the zero solution of
the system is stable; (2) if there exists a measurable set $E_2$ with positive
Lebesgue measure, such that $r(0)\in E_2$ implies that
$\lim\limits_{t\to+\infty}\tau(t)=+\infty$, then the zero solution of the
system is asymptotically stable. Furthermore, we establish a relationship
between the $i$th curvature $(i=1,2,\cdots)$ of the trajectory and the
stability of the zero solution when $A$ is similar to a real diagonal matrix.
