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This paper focuses on using curvature and torsion to describe the stabilityof linear time-invariant system. We prove that for a two-dimensional system$\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero isnot the limit of curvature of trajectory as $t\to+\infty$, then the zerosolution of the system is stable; (ii) if there exists an initial value, suchthat the limit of curvature of trajectory is infinity as $t\to+\infty$, thenthe zero solution of the system is asymptotically stable. For athree-dimensional system, (i) if there exists a measurable set whose Lebesguemeasure is greater than zero, such that for all initial values in this set,zero is not the limit of curvature of trajectory as $t\to+\infty$, then thezero solution of the system is stable; (ii) if the coefficient matrix isinvertible, and there exists a measurable set whose Lebesgue measure is greaterthan zero, such that for all initial values in this set, the limit of curvatureof trajectory is infinity as $t\to+\infty$, then the zero solution of thesystem is asymptotically stable; (iii) if there exists a measurable set whoseLebesgue measure is greater than zero, such that for all initial values in thisset, zero is not the limit of torsion of trajectory as $t\to+\infty$, then thezero solution of the system is asymptotically stable.

Description of Stability for Two and Three-Dimensional Linear Time-Invariant Systems Based on Curvature and Torsion