Global stabilisation in mean-square for stochastic time-delay uncertain systems via memoryless feedback

This article studies the problem of global stabilisation in mean-square for a class of stochastic uncertain systems with time-delay. Under the lower-triangular linear growth condition, it is proved that global exponential stabilisation (GES) in mean square of the stochastic nonlinear systems with a limited input delay and arbitrary large state delay is possible by memoryless feedback. A counterexample is constructed to show that without the linear growth condition, the considered system might not be GES in mean square by any memoryless feedback controller no matter how small the input delay is. By the feedback domination approach and the Lyapunov–Krasovskii functional method, a linear and delay-free feedback controller is constructed such that the stochastic time-delay nonlinear system is GES in mean square. Application of the memoryless control scheme to the one-link manipulator system with time-delay is given with simulation.