Output feedback control for low-order stochastic nonlinear time-delay systems

In this paper, we deal with the stabilization problem of a class of nonsmooth stochastic nonlinear time-delay systems via output feedback control. By extending the adding-a-power-integrator method of lower-triangular nonlinear systems and the Lyapunov-Krasovskii functional approach of time-delay nonlinear systems, a reduced-order observer based output feedback controller is developed to achieve the global strong asymptotic stability in probability of the resulting system. Compared with the existing methods, the considered system is continuous but nonsmooth and the power of chained integrators is arbitrary real numbers between 0 and 1. A numerical example is given to illustrate the effectiveness of the proposed methods.