Output-to-State Stability for systems on manifolds with multiple invariant sets

Output-to-State Stability(OSS) is a notion of detectability for nonlinear systems that is formulated in the ISS framework. We generalize the notion of OSS for systems evolving on manifolds and having multiple invariant sets. Building upon a recent extension of the Input-to-State Stability (ISS) theory for this very class of systems [1], the paper provides equivalent characterizations of the OSS property in terms of asymptotic estimates of the state trajectories and, in particular, in terms of existence of Lyapunov-like functions.