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
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
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 R^n just to name a few.
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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, pp.1--13. ⟨hal-01136819⟩

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