Stability Robustness in the presence of exponentially unstable isolated equilibria

David Angeli (1) , Laurent Praly (2)

1 DSI - Dipartimento di Sistemi e Informatica
2 CAS - Centre Automatique et Systèmes

This note studies nonlinear systems evolving on manifolds with a finite number of asymptotically stable equi- libria and a Lyapunov function which strictly decreases outside equilibrium points. If the linearizations at unstable equilibria have at least one eigenvalue with positive real part, 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.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

David Angeli, Laurent Praly. Stability Robustness in the presence of exponentially unstable isolated equilibria. 49th IEEE Conference on Decision and Control, Dec 2010, Atlanta, United States. pp.1581-1586, ⟨10.1109/CDC.2010.5717582⟩. ⟨hal-00554432⟩