Summary: This note presents an explicit proof of the theorem - due to Z. Artstein
[Nonlinear Anal., Theory Methods Appl. 7, 1163-1173 (1983; Zbl 0525.93053
)] - which states that the existence of a smooth control- Lyapunov function implies smooth stabilizability. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a ‘universal’ formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.