Smooth Output-to-State Stability for multistable systems on compact manifolds

¹ Department of Electrical and Electronic Engineering, Imperial College, London, UK
² Department of Information Engineering, University of Florence, Florence, Italy

^* Corresponding author: d.angeli@imperial.ac.uk

Received: 9 April 2021
Accepted: 25 March 2022

Abstract

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 which possess a decomposable invariant set and evolve on compact manifolds. Building upon a recent extension of the ISS theory for this very class of [systems [D. Angeli and D. Efimov, IEEE Trans. Autom. Control 60 (2015) 3242–3256.], 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 smooth Lyapunov-like functions.