For a given closed target we embed the dissipative relation that defines acontrol Lyapunov function in a more general differential inequality involvingHamiltonians built from iterated Lie brackets. The solutions of the resultingextended relation, here called degree-k control Lyapunov functions (k>=1), turnout to be still sufficient for the system to be globally asymptoticallycontrollable to the target. Furthermore, we work out some examples where nostandard (i.e., degree-1) smooth control Lyapunov functions exist while asmooth degree-k control Lyapunov function does exist, for some k>1. Theextension is performed under very weak regularity assumptions on the system, tothe point that, for instance, (set valued) Lie brackets of locally Lipschitzvector fields are considered as well.
展开▼
