Complete Stability Analysis With Respect to Delay for Neural Networks

The stability property of delayed neural networks (NNs) along the whole delay axis is studied in this paper. Such a complete stability problem with respect to the delay parameter has not been addressed in the community of NNs. Most of the existing studies focus on the stability interval of delay starting from zero and are not applicable for the complete stability problem. In this paper, we will present some examples to show that there are various types of stability intervals for NNs, demonstrating the necessity of the complete stability analysis. We will adopt a frequency-sweeping approach to study delayed NNs in this paper. As a result, the complete stability problem with respect to delay for NNs can be systematically solved. The approach is applicable in the general case and simple to implement. Finally, some representative examples illustrate the approach.