 LaSalle's invariance principle

On a compact positively invariant set where $\dot{V}\le 0$, every trajectory approaches the largest invariant subset of $\{\dot{V}=0\}$.

LaSalle's invariance principle is a fundamental result in the field of dynamical systems and control theory that provides conditions under which the behavior of a dynamical system can be analyzed in terms of its invariant sets. It is particularly useful in the study of stability for nonlinear systems.