Stabilisability of nonlinear systems by means of time-dependent switching rules

Given a family of linear systems which admit an asymptotically stable convex combination, the existence of stabilizing time-dependent switching rules can be proved by using the Baker-Campbell-Hausdorff formula for exponentials. The control laws obtained in this way are periodic, fast switching and independent of the initial state. We prove that under a similar assumption, the approach can be extended, to provide stabilizing timedependent switching rules for families of nonlinear vector fields, as well. However, the resulting control law in general is not periodic, not fast switching and it may depend on the initial state.