Mp. Joy et V. Tavsanoglu, CIRCULANT MATRICES AND THE STABILITY OF A CLASS OF CNNS, International journal of circuit theory and applications, 24(1), 1996, pp. 7-13
In this paper we show that feedback matrices of ring CNNs are block ci
rculants; as special cases, for example, feedback matrices of one-dime
nsional ring CNNs are circulant matrices. Circulants and their close r
elations the block circulants possess many pleasant properties which a
llow one to describe their spectrum completely. After deriving the spe
ctrum of the feedback operator, we discuss conditions for a CNN to be
contractive, ensuring global asymptotic stability.