Relaxation of the stability condition of the complex-valued neural networks

Jankowski et al. have proposed a complex-valued neural network (CVNN) that is capable of storing and recalling gray-scale images. However, the weight matrix of the CVNN must be Hermitian with nonnegative diagonal entries in order to preserve the stability of the network. The Hermitian assumption poses difficulties in both physical realizations and practical applications of the networks. In this letter, a new stability condition is derived. The obtained result not only permits a little relaxation on the Hermitian assumption of the connection matrix, but also generalizes some existing results.