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Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria

Abstract : This note studies nonlinear systems evolving on manifolds with a finite number of asymptotically stable equilibria and a Lyapunov function which strictly decreases outside equilibrium points. If the linearizations at unstable equilibria have at least one positive eigenvalue, then almost global asymptotic stability turns out to be robust with respect to sufficiently small disturbances in the L∞ norm. Applications of this result are shown in the study of almost global Input-to-State stability.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00643454
Contributeur : François Chaplais <>
Soumis le : lundi 21 novembre 2011 - 22:54:47
Dernière modification le : jeudi 24 septembre 2020 - 17:04:18

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David Angeli, Laurent Praly. Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2011, 56 (7), pp.1582 - 1592. ⟨10.1109/TAC.2010.2091170⟩. ⟨hal-00643454⟩

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