Stability in distribution of stochastic systems with high nonlinear delays under a new trigger mechanism

This paper delves into the issue of the asymptotic stability in distribution (ASID) and highly nonlinear event-triggered feedback control for stochastic delay systems with high nonlinearity. By introducing the event-triggered strategy into the state of the system, we establish the ASID of the input relative to the state of the system. Furthermore, we investigate both the ASID of a class of deterministic highly nonlinear delay systems with stochastic noise and discrete event-triggered stabilization, as well as the ASID of a class of stochastic highly nonlinear delay systems with discrete event-triggered stabilization. We find the upper limit of the duration τ∗ between two continuous state observations in a discontinuous observation. Utilizing Lyapunov functions and Itoˆ lemma, two bounded principles are established, and it is proved that the designed controller can ensure that the probability measure generated by the solution of the controlled system converges to the only probability measure that is the ASID. Finally, we present two examples to demonstrate the efficacy and accuracy of the methodologies utilized in this paper.