Attracting sets of discrete-time Markovian jump delay systems with stochastic disturbances via impulsive control

Abstract This paper investigates the exponential attracting sets of discrete-time Markovian jump delay systems (MJDSs) with stochastic disturbances (SDs) via impulsive control (IC). By virtue of the Lyapunov-Razumikhin technique, we derive several sufficient criteria on the pth moment exponential attracting sets of the impulsive controlled discrete-time MJDSs with SDs and the estimation of the attracting sets is also given. It is shown that IC could make both unbounded and bounded impulsive-free discrete-time MJDSs with SDs into the bounded ones. Examples are presented to illustrate the effectiveness of the proposed theoretical results.