Exponential Stability of Discrete-Time Markovian Jump Nonlinear Systems With Stochastic Impulses

This paper investigates the exponential stability (ES) of nonlinear discrete-time (DT) systems with stochastic impulses and Markovian jump. Employing the Lyapunov function method and the subsequence technique, the sufficient conditions for exponential stability of the
$pth$
moments (ES-
$pth$
) of the system are established. Generally, even if all the Markovian jump subsystems (MJSSs) are not ES-
$pth$
in the absence of impulses, impulses can still be used to achieve the ES-
$pth$
of the system in a specially designed interval, that is, when the impulses and Markovian jump signals meet the corresponding conditions. On the contrary, when all MJSSs are stable without impulses, as long as the impulses parameters and Markovian jump signals are relatively balanced, the system can still maintain the property of ES-
$pth$
. Finally, the effectiveness of results is further verified with three examples.