Lyapunov methods in nonsmooth optimization. Part II: Persistently exciting finite differences

For Part I see ibid. (2000). A recent converse Lyapunov theorem for differential inclusions is used to generate a class of finite difference algorithms for nonsmooth optimization. The algorithms rely on a proof of asymptotic stability for differential inclusions that contain persistently exciting signals and the ability to approximate these differential inclusions with finite differences. The notion of persistency of excitation that is used here generalizes that which is typically used in the identification and adaptive control literature