Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 31 | |
Number of page(s) | 53 | |
DOI | https://doi.org/10.1051/cocv/2022021 | |
Published online | 25 May 2022 |
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
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.
Mathematics Subject Classification: 93B07 / 93D05 / 93D20 / 93D25 / 34D23 / 34D35 / 34D45 / 37C70
Key words: Nonlinear stability / detectability / Output-to-State Stability / multistability / systems on manifolds
© The authors. Published by EDP Sciences, SMAI 2022
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