Exponential stability of stochastic impulsive switched delayed systems based on vector Lyapunov functions

In this paper, stochastic global exponential stability is studied for stochastic impulsive switched delayed systems. Two cases are investigated: the case that continuous dynamics is stable but the discrete dynamics is unstable and the case that the continuous dynamics is unstable but the discrete dynamics is stable. Using vector Lyapunov function and average dwell-time condition, stability conditions are derived for stochastic impulsive switched delayed systems. The obtained conditions allow the delay-free items and the time-delay items to be coupled. Finally, a numerical example of neural network is presented to illustrate the developed theory.