State feedback stabilisation for stochastic high-order feedforward nonlinear systems with input time-delay

This paper devotes to solve the problem of state feedback stabilisation for a class of stochastic high-order feedforward nonlinear systems with input time-delay. First, the delay-dependent control input is skillfully handled by using variable transformation technique. Then, by introducing the homogeneous domination approach and the appropriate Lyapunov--Krasovskii functional to deal with the time-delay, we construct a state feedback controller through a backstepping recursive design. It is shown that the proposed controller can guarantee the closed-loop system to be globally asymptotically stable (GAS) in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.