Output Feedback Stabilization of Stochastic Nonlinear Time-varying Delay Systems with Unknown Output Function

This paper addresses the problem of output feedback stabilization for stochastic nonlinear time-varying delay systems with an unknown output function. A remarkable feature of the system to be considered is the simultaneous presence of a continuous unknown sensitivity function and the stochastic disturbances, which have not been treated together before. A new observer is designed by using a dynamic gain without using the information on unknown time-varying delay and nonlinearities. With the aid of the observer, an output feedback controller is constructed by the stochastic double-domination method, where two gains are used to handle the unknown output function and nonlinearities. The performance of the system is analyzed in detail via two integral Lyapunov functions. Finally, the efficiency of the control strategy is illustrated by a simulation example.