Robust stochastic stability analysis for positive discrete-time Markov jump delay systems with delayed impulses

This paper is concerned with robust stochastic stability analysis for a class of positive discrete-time Markov jump delay systems (MJDSs) with partly known transition probabilities and delayed impulses. Some new results are given based on co-positive linear stochastic Lyapunov functionals. Firstly, a sufficient condition which guarantees that an unstable positive MJDS can be stochastically stable under certain stabilizing impulses is obtained. Then it is also shown that a stable positive MJDS can still remain its stochastic stability property with destabilizing impulses if the nearest impulsive time interval is appropriately large. Finally, a numerical example is given to illustrate the effectiveness of the present method.