Global stabilization of low-order stochastic nonlinear systems with multiple time-varying delays by a continuous feedback control

Abstract

The global stabilization problem is investigated in the present paper for a class of stochastic nonlinear systems, whose structure is in a p-normal form (0<p<1) and states are perturbed by multiple time-varying delays. By means of an extended stability theory of stochastic nonlinear time-delay systems, where the existence and uniqueness of strong solution of an initial value problem is not required, a nonsmooth but continuous delay-dependent global stabilizer is systematically constructed to achieve the global strong asymptotic stability in probability of the closed-loop system under some conditions. In order to overcome the obstacles caused by low-order nonlinear terms, multiple time-varying delays and stochastic disturbances, a novel nonlinear Lyapunov-Krasovskii functional is skillfully introduced, which plays an important role in the controller design. The effectiveness of the obtained results is verified by an illustrative example in the end.