The ISS approach to the stability and robustness properties of nonautonomous systems with decomposable invariant sets: An overview

This paper is an overview of recent developments in the Input-to-State Stability framework, dealing in particular with the extension of the classical concept to systems with multiple invariant sets and possibly evolving on Riemannian manifolds. Lyapunov-based characterizations of the properties are discussed as well as applications to the study of cascaded nonlinear systems.