2016
DOI: 10.1016/j.ejcon.2016.04.003
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The ISS approach to the stability and robustness properties of nonautonomous systems with decomposable invariant sets: An overview

Abstract: This article is an overview of recent developments in the Input-to-State Stability framework, dealing in particular with the extension of the classical concept to systems with multiple invariant sets and possibly evolving on Riemannian manifolds. Lyapunov-based characterizations of the properties are discussed as well as applications to the study of cascaded nonlinear systems.

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Cited by 9 publications
(8 citation statements)
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“…y T ϕ(y) ≥ ε|y| 2 , ∀y ∈ Y, ε > 0. (15) If the condition (15) is satisfied and the function β ∈ K∞ or |h(x)| ≥ ̺(|x|W ) for all x ∈ M, then the control (13) guarantees ISS property with respect for the set W and the disturbance input v, and V is an ISS-Lyapunov function.…”
Section: Resultsmentioning
confidence: 99%
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“…y T ϕ(y) ≥ ε|y| 2 , ∀y ∈ Y, ε > 0. (15) If the condition (15) is satisfied and the function β ∈ K∞ or |h(x)| ≥ ̺(|x|W ) for all x ∈ M, then the control (13) guarantees ISS property with respect for the set W and the disturbance input v, and V is an ISS-Lyapunov function.…”
Section: Resultsmentioning
confidence: 99%
“…Let a passive system (10), (11) admit Assumption 2. If the control (13) is applied under (15) and an additional restriction:…”
Section: Resultsmentioning
confidence: 99%
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“…Following the results of [33], the authors in [45] have provided conditions for the robust synchronization of multistable systems in the presence of external inputs. Readers can consult [46] for an overview of recent developments in the ISS framework, dealing in particular with the extension of the classical concept to systems with multiple invariant sets and possibly evolving on Riemannian manifolds.…”
Section: Introductionmentioning
confidence: 99%
“…inequalities, generalizing the classical ISS theory [30], [31], [8], [3], [15]. In its turn, integral input-to-state stability (iISS) characterization, which is weaker than the classical one given in [29], [21], [5], was extended in [16] for systems with multiple invariant sets.…”
Section: Introductionmentioning
confidence: 99%