Stability of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities

In this paper, stochastic stability for a class of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities is investigated. Some new results are given based on stochastic Lyapunov functionals. It is shown that an unstable discrete-time Markovian jump delay system can be stochastically stable under certain stabilizing impulses. It is also shown that, when the nearest impulsive time interval is appropriately large, a stable discrete-time Markovian jump delay system can retain its stochastic stability property even with destabilizing impulses. Numerical examples together with their simulations are provided to demonstrate the effectiveness of the derived results.