Delay Feedback Control Based on Discrete-time State Observations for Highly Nonlinear Hybrid Stochastic Functional Differential Equations With Infinite Delay

In this paper, it is proved that an unstable highly nonlinear hybrid stochastic functional differential equation with infinite delay (HNHISFDE) can be stabilized by designing a controller that not only depends on discrete-time state observations, but only produces different time lags in each observation. Firstly, common conditions are imposed on the original system to ensure the existence and uniqueness of the solution. Secondly, the design method of delay feedback control is presented to stabilize a class of HNHISFDEs. Notably, new assumptions based on Lyapunov functional and M-matrix methods are provided to construct the controller step by step. Then, the sufficient criteria of H infinity stabilization, asymptotic stabilization and exponential stabilization are established by applying the Lyapunov stability theory. Finally, the effectiveness of the theoretical results is illustrated by a numerical example.