Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria
Authors: David Angeli , Laurent Praly, IEEE Transactions on Automatic Control, Vol 56, no 7, pp. 1582 - 1592, DOI: 10.1109/TAC.2010.2091170
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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BibTeX:
@Article{,
author = {Laurent Praly David Angeli },
title = {Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria},
journal = {IEEE Transactions on Automatic Control},
volume = {56},
number = {7},
pages = {1582 - 1592},
year = {2011},
}
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.
Download PDF
BibTeX:
@Article{,
author = {Laurent Praly David Angeli },
title = {Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria},
journal = {IEEE Transactions on Automatic Control},
volume = {56},
number = {7},
pages = {1582 - 1592},
year = {2011},
}