Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria

David Angeli (1) , Laurent Praly (2)

1 DEEE - Department of Electrical and Electronic Engineering [London]
2 CAS - Centre Automatique et Systèmes

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.

Mots clés: Almost global stability; gradient-like systems; input-to-state stability; integral manifolds; nonlinear systems on manifolds

Domaines: Automatique / Robotique

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