Stabilisation of coupled delayed regime‐switching diffusion with continuous‐state‐dependent switching via intermittent control

Abstract

Motivated by Markovian regime-switching diffusion (MRSD), time-varying delays and non-linear coupling forms, this study is concerned with stabilisation of coupled regime-switching diffusion with time-varying delays (CRSDTD) under periodically intermittent control. Compared with most papers investigating MRSD, a striking feature of regime-switching diffusion is that in the two-component process ( x ( t ) , α ( t ) ) , switching process α ( t ) depends on the diffusion x ( t ) , which can be regarded as the x-dependent process briefly. It is worth mentioning that time-varying delays and non-linear coupling forms are taken into consideration when modelling, which makes their work more realistic. Moreover, a periodically intermittent controller is adopted to guarantee that CRSDTD can achieve the pth moment exponential stability and some sufficient conditions are derived by using the Lyapunov method and Kirchhoff's matrix tree theorem. Furthermore, to illustrate the applicability of their theoretical results, an application to regime-switching coupled oscillators with time-varying delays (RSCOTD) is presented and a stability criterion is given. Conclusively, numerical simulations on RSCOTD are presented to illustrate the effectiveness of the theoretical results.