Skip to Main content Skip to Navigation
Journal articles

Characterizations of Input-to-State Stability for systems with multiple invariant sets

David Angeli 1, 2 Denis Efimov 3
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : We generalize the theory of Input-to-State Stability (ISS) and of its characterizations by means of Lyapunov dissipation inequalities to the study of systems admitting invariant sets, which are not necessarily stable in the sense of Lyapunov but admit a suitable hierarchical decomposition. It is the latter which allows to greatly extend the class of systems to which ISS theory can be applied, allowing in a unified treatement to deal with oscillators in Euclidean coordinates, almost globally asymptotically stable systems on manifolds, systems with multiple equilibria in $\mathbb{R}^n$ just to name a few.
Document type :
Journal articles
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.inria.fr/hal-01136819
Contributor : Denis Efimov Connect in order to contact the contributor
Submitted on : Monday, March 30, 2015 - 12:03:40 PM
Last modification on : Friday, January 21, 2022 - 3:23:03 AM
Long-term archiving on: : Thursday, July 2, 2015 - 9:01:06 AM

File

conjectureisslike30.pdf
Files produced by the author(s)

Identifiers

Citation

David Angeli, Denis Efimov. Characterizations of Input-to-State Stability for systems with multiple invariant sets. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2015, 60 (12), pp.3242 - 3256. ⟨10.1109/TAC.2015.2418676⟩. ⟨hal-01136819⟩

Share

Metrics

Les métriques sont temporairement indisponibles