Stability of hybrid stochastic delay systems whose discrete components have a large state space: A two-time-scale approach

This work is concerned with stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain has a large state space and is subject to both fast and slow movements. Under simple conditions, we demonstrate that if the limit systems are pth-moment exponentially stable, then the original systems are pth-moment exponentially stable in an appropriate sense. In addition, the exponential stability is also investigated. Moreover, stability in distribution is obtained for such hybrid systems.