Séance Séminaire

Séminaire ACSIOM

Stability of Nonlinear Switched Systems

Let $X$ and $Y$ be two smooth vector fields on $R^2$ , globally asymptotically stable at the origin, and consider the nonlinear system $q =uX+(1-u)Y$, where $u:[0,\infty)\to {0,1}$ is an arbitrary measurable function. Analyzing the topology of the set where $X$ and $Y$ are parallel, I 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 do not change under small perturbations of the vector fields