A new stability condition for discrete time recurrent neural networks with complex-valued linear threshold neurons

This paper discusses the stability condition for discrete time recurrent neural networks (RNNs) with complex-valued linear threshold (CLT) neurons. The energy-function method is very useful for complex-valued RNNs study, especially for multi-stable RNNs. In addition to properties of CLT RNNs discussed in earlier work, a new stability condition is offered here by virtue of a lower-bounded energy function. Simulation results are presented to illustrate the theory.

I. Introduction

Complex number calculus has been very useful in many applied technology areas, such as electrical engineering, informatics, control engineering, and so on. Complex-valued neural networks (NNs), which have complex-valued weights and neuron activation functions, can deal with complex-valued data. Significant amount of work has been done in complex-valued NNs in recent years [1], [2].