New stability condition for discrete-time fully coupled neural networks with multivalued neurons

This paper discusses the stability condition for discrete-time multi-valued recurrent neural networks (MVNRNNs) in asynchronous update mode. In the existing research literature, an MVNRNN in asynchronous update mode has been found convergent if its weight matrix is Hermitian with nonnegative diagonal entries. However, our finding has been that the weight matrix with zero diagonal entries cannot guarantee the network stability. Furthermore, the new stability condition and proof is offered to allow diagonal entries to be complex-valued, which extends previous theoretical result. Simulation results are used to illustrate the theory.