Further results on the global asymptotic stability of neural networks

The classes of I₀-stable matrices (denoted by I₀ ) and additively diagonally stable matrices (denoted by M₀ ) are important in the context of the analysis of absolute stability (ABST) of neural networks. In comments by Kaszkurewicz and Bahaya (see IEEE Trans. Circuits Syst.-I, vol. 42, p. 497-499, August 1995), it was conjectured that the I₀ condition of the interconnection matrix T of a neural network is a necessary and sufficient condition for the neural network to be absolutely stable. In a reply by the authors (see IEEE Trans. Circuits Syst.-I, vol. 45, p. 595-596, May 1998) to these comments, it is shown that the M₀ condition on T is a sufficient condition for ABST. In this paper the authors clarify the relationship between the classes I₀ and M ₀. It is proved by an example that the class M₀ is a strict subclass of class I₀, leading us to draw new conclusions on ABST of neural networks. They also give an example which disproves the conjecture made by Kaszkurewicz and Bhaya