2005/02/16 by Ugo Boscain, Boscain, Ugo, Grégoire Charlot +3
Mathematics · #34D05 #34D23 #93C10 #93D20 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:34D05 #msc:34D23 #msc:93C10 #msc:93D20
paper · pdf · doi:10.48550/arxiv.math/0502361
arxiv created 2005/02/16 · arxiv updated 2016/08/16
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 %C^∞ 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.