Stability and Synchronization of Switched Multi-Rate Recurrent Neural Networks

Abstract

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. INDEX TERMSRecurrent neural networks, multi-rate systems, switched systems, Lyapunov methods.

Global attractive set of neural networks with neutral item

“…According to different application requirements, its dynamic characteristics have different requirements. Many scholars have some interesting conclusions in this area [9,17,18]. Especially, the global exponential stability of several types of neural networks is discussed in [2,4,5].…”