Stability of Planar Nonlinear Switched Systems

Abstract : We consider the time-dependent nonlinear system $\dot q(t)=u(t)X(q(t))+(1-u(t))Y(q(t))$, where $q\in\R^2$, $X$ and $Y$ are two %$C^\infty$ smooth vector fields, globally asymptotically stable at the origin and $u:[0,\infty)\to\{0,1\}$ 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.
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Submitted on : Wednesday, February 16, 2005 - 6:24:28 PM
Last modification on : Friday, January 18, 2019 - 1:19:49 AM
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Ugo Boscain, Grégoire Charlot, Mario Sigalotti. Stability of Planar Nonlinear Switched Systems. 2005. ⟨hal-00004272⟩

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