Universal formulas for CLFs with respect to Minkowski balls

Abstract

This note provides explicit, algebraic stabilizing formulas for control Lyapunov functions when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a theorem of Artstein (1995), but the proof of Artstein's theorem is nonconstructive. The formulas are used to construct approximation solutions to some stabilization problems.