Asymptotic feedback controllability of switched control systems to the origin

Trajectories of controllable switched systems consisting of linear continuous-time time-invariant subsystems are arbitrarily closely approximated by those of a controllable time-invariant non-switched polynomial systems. Examples are obtained to show that the aforementioned switched control systems are not locally asymptotically stabilizable via continuous switching strategies. Finally, asymptotic feedback controllability of such switched control systems is established.