Feedback delay control of highly nonlinear stochastic functional differential equations with discrete-time state observations

The purpose of this paper is to give the delay control based on discrete‐time state observations to stabilize highly nonlinear hybrid stochastic functional differential equations (SFDEs). It is considered that time lag generated by the controller in each discrete observation should be different. The new controlled hybrid SFDEs are affected the variable delay caused by the controller, the distributed delay, and the superlinear coefficients of the systems itself, which makes the problem handling more complicated. Then, a series of criteria for the exponential stability of the controlled SFDEs are obtained, and an upper bound for the discrete observation interval and variable delay is given. Finally, numerical example illustrates the proposed theoretical results.