A proof of Kaszkurewicz and Bhaya's conjecture on absolute stability of neural networks in two-neuron case

This letter presents a proof of Kaszkurewicz and Bhaya's conjecture (1995) on the absolute stability of neural networks in the two-neuron case. The conjecture states that the necessary and sufficient condition for absolute stability of neural networks with an n/spl times/n interconnection matrix T is T/spl isin/I/sub 0/, where I/sub 0/ denotes the class of matrices T such that matrix (T-D/sub 1/)D/sub 2/ has all eigenvalues with negative real parts for arbitrary positive diagonal matrices D/sub 1/ and D/sub 2/. A characterization condition for the I/sub 0/ class of matrices in the two-dimensional (2-D) case n=2 is also obtained.