Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable

This brief paper investigates the problem of output-feedback stabilization for a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the ideas of the homogeneous systems theory and the adding a power integrator technique, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable (GAS) in probability. The efficiency of the output-feedback controller is demonstrated by a simulation example.