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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.