Almost sure stability of discrete-time nonlinear Markovian jump delayed systems with impulsive signals

This study investigates the almost sure stability for a class of discrete-time nonlinear Markovian jump delayed systems with impulsive signals, where delay and external input exist in continuous and discrete dynamics. Sufficient conditions that guarantee the almost sure stability for a delayed impulsive Markovian jump system are established by using Lyapunov function method and the subsequence technique. Although all the Markovian jump subsystems are not almost surely stable in the case of no impulses, impulses can be devoted to achieving the almost sure stability of the system in a specially designed interval, that is, the impulsive and Markovian jump signals satisfy the upper length of dwell time condition. Conversely, when all the Markovian jump subsystems are almost surely stable in the absence of impulses, then the system can still retain the properties of almost sure stability when the impulse parameters remain in a limited range. In addition, the combination of the first and second cases are considered in this study. Results can be applied to systems with arbitrary large time delays. Several effective examples are also presented to illustrate the main results. (C) 2019 Elsevier Ltd. All rights reserved.