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Journal Articles IEEE Transactions on Automatic Control Year : 2015

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

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.

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Automatic
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Dates and versions

hal-01136819 , version 1 (30-03-2015)

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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, 2015, 60 (12), pp.3242 - 3256. ⟨10.1109/TAC.2015.2418676⟩. ⟨hal-01136819⟩
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