Stabilization of Artstein´s circle by continuous stochastic feedback

This paper presents the asymptotic stabilization of the Artstein´s circle using stochastic processes in a control law. To construct a C² control Lyapunov function (CLF) for a stabilization method using stochastic processes, we synthesize a nonsmooth CLF for a nonsmooth stabilization method and a smooth function. By synthesizing these functions, we obtain a C² CLF. By this C² CLF, we can obtain a continuous stabilizing feedback using stochastic processes for the Artstein´s circle.