Аннотация:The authors consider the perturbed system x=f(t,x)+μR(t,x), assuming that (i) the unperturbed system x=f(t,x) has a stale equilibrium x=0, and there exists a positive-definite function V(t,x) with an infinitesimal higher limit. Stability is deduced in two ways: from the assumption that V(t,x) is a Lyapunov function, and from a comparison argument based on the definition V(t,x)=max i V i (t,v).