Smooth Output-to-State Stability for multistable systems on compact manifolds
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 31

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.

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DOI : 10.1051/cocv/2022021
Classification : 93B07, 93D05, 93D20, 93D25, 34D23, 34D35, 34D45, 37C70
Keywords: Nonlinear stability, detectability, Output-to-State Stability, multistability, systems on manifolds 
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     author = {Forni, Paolo and Angeli, David},
     title = {Smooth {Output-to-State} {Stability} for multistable systems on compact manifolds},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {28},
     doi = {10.1051/cocv/2022021},
     mrnumber = {4428678},
     zbl = {1490.93110},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2022021/}
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Forni, Paolo; Angeli, David. Smooth Output-to-State Stability for multistable systems on compact manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 31. doi: 10.1051/cocv/2022021

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