Stability condition for discrete time multi-valued recurrent neural networks in asynchronous update mode

This paper discusses the stability condition for discrete time multi-valued (MVN) recurrent neural networks in asynchronous update mode. In existing research literature, the MVN network in asynchronous update mode has been found convergent if its weight matrix is Hermitian with nonnegative diagonal entries. However, the new theorem and proof presented here show that weight matrix with zero diagonal entries can´t guarantee the network stability. Simulation results are used to illustrate the theory.