Boscain, UgoCharlot, GrégoireSigalotti, Mario20052011-09-0720052011-09-072005Discrete Contin. Dyn. Syst. 15 (2006) 415-432https://openscience.sissa.it/handle/1963/1710We 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.322404 bytesapplication/pdfen-USPreprint