Stabilization of hybrid stochastic differential equations with multiple delays via intermittent control

In this paper, we study stability of hybrid stochastic differential equations (SDEs) with multiple delays by intermittent control based on time-varying delay observations. By constructing an auxiliary non-delayed hybrid stochastic differential equation and using M$$ M $$-matrix theory, Lyapunov method, and the comparison principle, sufficient criterions to guarantee the q$$ q $$th moment exponential stability and almost sure exponential stability of hybrid SDEs are derived. Finally, a simulation example is shown to illustrate the validity of theoretical results.

Automated summary

This paper studies the stability of hybrid stochastic differential equations with multiple delays by intermittent control and time-varying delay observations. Sufficient criteria for ensuring the q-th moment exponential stability and almost sure exponential stability of the hybrid SDEs are derived using M-matrix theory, Lyapunov method, and the comparison principle. A simulation example is provided to illustrate the validity of the theoretical results.