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

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. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.