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

Abstract

In this paper, the output feedback stabilization problem is investigated for a class of low-order stochastic nonlinear time-delay systems with the lowertriangular 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. Nevertheless, we show that an output feedback controller can be systematically designed to ensure the global strong asymptotic stability of the closed-loop system based on an extended stochastic stability theory. 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, a numerical example is provided to verified the effectiveness of the proposed method. KeywordsOutput feedback stabilization • Low-order nonlinearities • Stochastic nonlinear systems • State observer • Multiple time-varying delays J. Jia ( ) • F. Zhang ( ) •