New necessary and sufficient conditions for absolute stability of neural networks

This paper presents new necessary and sufficient conditions for absolute stability of neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. It also demonstrates how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that it is applicable to a class of neural networks with non-normal weight matrices.