Stability and synchronization for impulsive Markovian switching CVNNs: matrix measure approach

•By introducing Markov chain, the model under consideration is more real in practice. The results obtained show that the noise has great influence on the stability and synchronization of the network with Markov chain taking values in the finite state space.•Furthermore, the matrix measure approach has been utilized to deal with the problem. The advantage of this method is to effectively deal with the system without constructing any Lyapunov functions, and hence new and convenient.•Finally, the impulsive control scheme has been utilized to realize to synchronization for the coupled complex-valued neural networks, which is more challenging and hence should obtain much attention.