@article {2006,
title = {Stability of planar nonlinear switched systems},
number = {SISSA;04/2005/M},
year = {2006},
abstract = {We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 - u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,$\infty$) {\textrightarrow} {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.},
url = {http://hdl.handle.net/1963/1710},
author = {Ugo Boscain and Gr{\'e}goire Charlot and Mario Sigalotti}
}