Smooth Lyapunov Functions for Multistable Differential Inclusions

We provide a converse Lyapunov theorem for differential inclusions with upper semicontinuous right-hand side, admitting a finite number of compact, globally attractive, weakly invariant sets, and evolving on Riemannian manifolds. Such properties entail multistable behavior in differential inclusions and may gather interest in a number of applications where uncertainty and discontinuities of the vector field play a major role