Stabilization of highly nonlinear hybrid stochastic differential delay equations by periodically intermittent feedback controls based on discrete-time observations with asynchronous switching

TL;DR

This paper develops a control strategy for highly nonlinear hybrid stochastic delay systems, ensuring their exponential stabilization using intermittent feedback based on discrete observations, with proven bounds and convergence properties.

Contribution

It introduces a novel intermittently controlled stabilization method for complex stochastic delay systems with asynchronous switching, providing theoretical bounds and stability analysis.

Findings

Established boundedness of the solution's moments.

Proved exponential stability and convergence rate.

Showed control interval proportion affects convergence rate.

Abstract

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the $p$-th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.