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This paper focuses on using the first curvature $\kappa(t)$ of trajectory todescribe the stability of linear time-invariant system. We extend the resultsfor 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 measureis 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 ofthe system is stable; (ii) if the matrix $A$ is invertible, and there exists ameasurable set whose Lebesgue measure is greater than zero, such that for allinitial values in this set, $\lim\limits_{t\to+\infty}\kappa(t)=+\infty$, thenthe zero solution of the system is asymptotically stable.

Description of Stability for Linear Time-Invariant Systems Based on the First Curvature