Stability Analysis of Stochastic Delay Systems with Markov Switching and Delayed Impulses

The p-th moment exponential stability problem was investigated for stochastic delayed systems with Markovian switching and delayed impulses. Sufficient conditions for p-th moment exponential stability were established based on the Lyapunov−Krasovskii theory and the average impulsive interval theory. Time-delays were considered in both the continuous dynamics and the impulsive actions. An appropriate Lyapunov−Krasovskii functional was constructed, and constraints were imposed on its differential operator.The conservatism of the stability criteria was effectively reduced by combining the average impulsive control strategy to regulate the frequency and intervals of impulses. The validity of the theoretical results was verified through numerical simulations.The results indicate that delayed impulses exhibit a dual effect on system stability, where stabilizing delayed impulses promote stability while destabilizing delayed impulses adversely affect it. Particularly, under destabilizing delayed impulses, the transition probabilities of the Markov chain are found to influence the system's decay rate. The overall decay rate can be modified by properly adjusting the transition probabilities between subsystems, thereby achieving system stability. Specifically, the p-th moment exponential stability is effectively guaranteed when the transition probability from unstable subsystems to stable ones is sufficiently large, while the transition probability from stable subsystems to unstable ones is sufficiently small.