Necessary and sufficient condition for absolute exponential stability of a class of nonsymmetric neural networks
Xue Liang, Toru Yamaguchi · Civil War Book Review · 1997
In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al.[1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al.[1]. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.