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A set of stability criteria for delayed cellular neural networks. (English) Zbl 0994.82066
Summary: This brief article presents a set of criteria on the global asymptotic stability of delayed cellular neural networks by constructing suitable Lyapunov functionals, introducing ingeniously real parameters $w_i>0, \alpha_{ij}^*,\beta_{ij}^*,\eta_{ij}^*, \zeta_{ij}^*,\alpha_{ij},\beta_{ij},\eta_{ij},\zeta_{ij}\in R$ with $\alpha_{ij}^*+\beta_{ij}^*=1, \alpha_{ij}+\beta_{ij}=1, \eta_{ij}^*+\zeta_{ij}^*=1,\eta_{ij}+\zeta_{ij}=1$ ($i,j=1,2,\dots,n$) and combining this with the elementary inequality $2ab\le a^2+b^2$. These criteria are of important theoretical and applicable significance in signal processing, especially in speed detection of moving objects, processing of moving images and the design of networks since they possess infinitely adjustable real parameters. This result is also discussed from the point of view of its relationship to earlier results.

##### MSC:
 82C32 Neural nets (statistical mechanics) 78A55 Technical applications of optics and electromagnetic theory 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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