Global stability analysis of discrete-time recurrent neural networks

We address the problem of Lyapunov stability of discrete-time recurrent neural networks (RNN). We assume that network weights are fixed. Based on classical results of the theory of absolute stability, we propose a new approach to stability analysis of RNN with sector-type monotone nonlinearities. We devise a simple state space transformation to convert the original RNN equations to a form suitable for our stability analysis. We then write appropriate linear matrix inequalities (LMI) to be solved to determine whether the RNN is globally exponentially stable. Unlike previous treatments, our approach naturally permits to account for nonzero biases usually present in RNN for improved approximation capabilities. We illustrate how to use our approach with an example