Stabilization problems of nonlinear systems using feedback laws with Wiener processes

This paper proposes a method to stabilize the origins of deterministic dynamical systems by state feedback control laws with Wiener processes. First, we obtain Ito-type stochastic dynamical systems by randomizing ordinary differential equation systems. Second, we design the diffusion coefficients. Then, we obtain Sontag-type global asymptotically stabilizers based on the stochastic control Lyapunov functions. Moreover, we show the usefulness of our results by some examples, i.e., systems with noncontractible state spaces and nonholonomic systems.