= Quasi-asymptotic stability
An <equilibrium point> is quasi-asymptotically stable when some neighborhood of initial conditions has forward solutions converging to it. This attraction condition alone does not include <Lyapunov stability>. <Asymptotic stability> requires both attraction and Lyapunov stability. A positive <Lyapunov function> with nonpositive derivative and no nonstationary invariant trajectory in its zero-derivative set proves both when its sufficiently small sublevel sets are compact and forward invariant.
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