Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

In this paper, the output feedback stabilization problem is investigated for a class of low-order stochastic nonlinear time-delay systems with the lower-triangular form, where the powers of chained integrators are arbitrary real numbers between 0 and 1, and the multiple time-vary delays act on each system state. Because of the existence of low-order nonlinear terms, the system is not feedback linearizable and differentiable. Based on an extended adding a power integrator approach and a stability theory of stochastic continuous systems, an output feedback controller is systematically designed to ensure the global strong asymptotic stability of the closed-loop system. In the controller design, the negative effect of the multiple time-varying delays is counteracted by skillfully constructing a novel Lyapunov-Krasovskii functional, and the observer gains are determined by developing a recursive selection procedure. Finally, two numerical examples are provided to verify the effectiveness of the proposed method.