A Lyapunov–Razumikhin control strategy for stochastic nonlinear delayed systems with polynomial conditions

Numerous control schemes for stochastic systems involving time-varying delays need a strict slow time-delay condition, which does hold for some practical models. Also, some stochastic systems will have different structures as working conditions change. In this article, we will investigate the control of stochastic systems which contain time-varying delays and polynomial conditions. By providing the dynamic-gain based homogeneous domination approach, and selecting a new Lyapunov–Razumikhin (L–R) function, a universal dynamic controller for systems with different growing conditions is presented, and the slow time-delay condition is removed successfully. The algorithm is finally verified with a practical example.