A new stability condition for discrete time linear threshold recurrent neural networks

This paper discusses the stability condition for discrete time recurrent neural networks (RNNs) with linear threshold (LT) neurons. In the existing research literature [1], the LT RNN in synchronous update mode is completely convergent if I-W is a copositive matrix. However, this condition also requires that W should be symmetrical. Here, a new stability condition is presented, which extends previous theoretical result first published in [1], and allows LT RNN to be stable when W is unsymmetrical in some cases. Simulation results are used to illustrate the theory.