Stability of stochastic delayed semi-Markov jump systems with stochastic mixed impulses: A novel stochastic impulsive differential inequality

In this paper, the pth moment exponential stability of stochastic delayed systems is studied. It is worth mentioning that semi-Markov jump and stochastic mixed impulses are considered simultaneously in the stochastic delayed systems. Besides, a new impulsive differential inequalities with semi-Markov jump and stochastic mixed impulses are established. The method of graph theory, stochastic analysis technique and Lyapunov method are cleverly combined, which contributes to propose stability criteria for stochastic delayed semi-Markov jump systems with stochastic mixed impulses. Finally, the theoretical results are applied to a kind of oscillator systems. The simulation results verify the effectiveness of the theoretical results.