Simultaneous stabilization for a collection of stochastic nonlinear systems based on CLFs

This paper investigates the simultaneous stabilization of a collection of single-input nonlinear stochastic systems. Based on the generalized stochastic Lyapunov theorem and the technique of control Lyapunov functions, we first present a universal formula for constructing continuous stabilizing feedback for control stochastic differential equations, this result extends Sontag's theorem to nonlinear control systems corrupted by noise. Next a simultaneous stabilization controller is designed.