On the stability of the cellular neural networks with time lags

Abstract

Cellular neural networks (CNNs) are recurrent artificial neural networks. Due to their cyclic connections and to the neurons’ nonlinear activation functions, recurrent neural networks are nonlinear dynamic systems, which display stable and unstable fixed points, limit cycles and chaotic behavior. Since the field of neural networks is still a young one, improving the stability conditions for such systems is an obvious and quasi-permanent task. This paper focuses on CNNs affected by time delays. We are interested to obtain sufficient conditions for the asymptotical stability of a cellular neural network with time delay feedback and zero control templates. For this purpose we shall use a method suggested by Malkin (1952), where the “exact” Liapunov-Krasovskii functional will be constructed according the procedure proposed by Kharitonov (2001) for stability analysis of uncertain linear time delay systems.