%0 Report
%D 2006
%T Stability of planar nonlinear switched systems
%A Ugo Boscain
%A Grégoire Charlot
%A Mario Sigalotti
%X 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,∞) → {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.
%B Discrete Contin. Dyn. Syst. 15 (2006) 415-432
%G en_US
%U http://hdl.handle.net/1963/1710
%1 2441
%2 Mathematics
%3 Functional Analysis and Applications
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