Two categories of new criteria of pth moment stability for switching and impulsive stochastic delayed functional differential equation with markovian switching

This note focuses on the pth moment stability for switching and impulsive stochastic delayed functional differential equation with Markovian switching. Under delay and Markovian switching, several novel stability criteria of pth moment input-to-state stability and pth moment integral input-to-state stability are enumerated by wielding Razumikhin/Krasovskii stability theory. Meanwhile, we show the correlation and differences for Razumikhin and Krasovskii method. The characteristic of the criteria requires that the time derivatives of the Razumikhin or Krasovskii functionals are enabled to be a function of time various, which can slacken guard in requirement. It is shown that, if the subsystems are stable in some interval but the discrete dynamics are not, the stochastic delayed hybrid system is stable. On the contrary, when the jump maps are stable with uncertain subsystems, the delayed-dependent impulses may overcome the destabilizing effects to achieve the stability. Finally, an example is given to show the effectiveness and practicability of the results. © 2022 The Franklin Institute