Several designs of recurrent neural networks have been proposed in the literature involving different clock times. However, the stability and synchronization of this kind of system have not been studied. In this paper, we consider that each neuron or group of neurons of a switched recurrent neural network can have a different sampling period for its activation, which we call switched multi-rate recurrent neural networks, and we propose a dynamical model to describe it. Through Lyapunov methods, sufficient conditions are provided to guarantee the exponential stability of the network. Additionally, these results are extended to the synchronization problem of two identical networks, understanding the synchronization as the agreement of both of them in time. Numerical simulations are presented to validate the theoretical results. The proposed method might help to design more efficient and less computationally demanding neural networks.
