00968nas a2200121   4500008004300000245005100043210005100094520060400145100001700749700002300766700002100789856003600810       2006                        en_Ud  00aStability of planar nonlinear switched systems0 aStability of planar nonlinear switched systems3 aWe 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,∞) → {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.1 aBoscain, Ugo1 aCharlot, Grégoire1 aSigalotti, Mario  uhttp://hdl.handle.net/1963/1710