TY - RPRT
T1 - Stability of planar nonlinear switched systems
Y1 - 2006
A1 - Ugo Boscain
A1 - Grégoire Charlot
A1 - Mario Sigalotti
AB - 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.
JF - Discrete Contin. Dyn. Syst. 15 (2006) 415-432
UR - http://hdl.handle.net/1963/1710
U1 - 2441
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -