Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays

In this paper, we investigate the adaptive output-feedback stabilisation for a class of stochastic non-linear systems with time-varying time delays. First, we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non-linear systems with time delays, and introduce a new stability notion and the related criterion. Then, for a class of stochastic non-linear systems with time-varying time delays, uncertain parameters in both drift and diffusion terms, and general constant virtual control coefficients, we present a systematic design procedure for a memoryless adaptive output-feedback control law by using the backstepping method. It is shown that under the control law based on a memoryless observer, the closed-loop equilibrium of interest is globally stable in probability, and moreover, the solution process can be regulated to the origin almost surely.