Stability Robustness in the presence of exponentially unstable isolated equilibria
Authors: David Angeli, Laurent Praly, 49th IEEE Conference on Decision and Control, pp. 1581-1586, December 15-17, 2010, Atlanta DOI: 10.1109/CDC.2010.5717582
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 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.
Download PDF
BibTeX:
@Proceedings{,
author = {David Angeli, Laurent Praly},
editor = {},
title = {Stability Robustness in the presence of exponentially unstable isolated equilibria},
booktitle = {49th IEEE Conference on Decision and Control},
volume = {},
publisher = {IEEE},
address = {Atlanta},
pages = {1581-1586},
year = {2010},
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 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.},
keywords = {}}
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 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.
Download PDF
BibTeX:
@Proceedings{,
author = {David Angeli, Laurent Praly},
editor = {},
title = {Stability Robustness in the presence of exponentially unstable isolated equilibria},
booktitle = {49th IEEE Conference on Decision and Control},
volume = {},
publisher = {IEEE},
address = {Atlanta},
pages = {1581-1586},
year = {2010},
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 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.},
keywords = {}}