Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria

Author

Angeli, David ; Praly, Laurent

Author_Institution

Dept. of Electr. & Electron. Eng., Imperial Coll., London, UK

Volume

56

Issue

7

fYear

2011

fDate

7/1/2011 12:00:00 AM

Firstpage

1582

Lastpage

1592

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.

Keywords

Lyapunov methods; asymptotic stability; linearisation techniques; nonlinear control systems; robust control; Lyapunov function; eigenvalue; exponentially unstable isolated equilibria; global asymptotic stability robustness; global input-to-state stability; linearizations; nonlinear systems; outside equilibrium points; Asymptotic stability; Eigenvalues and eigenfunctions; Lyapunov method; Manifolds; Nonlinear systems; Robustness; Stability analysis; Almost global stability; gradient-like systems; input-to-state stability; integral manifolds; nonlinear systems on manifolds;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2091170

Filename

5658110