Stability Results for Cellular Neural Networks with Time Delays

Abstract

Cellular neural networks (CNNs) introduced by Chua and Yang in 1988 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 recent 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 asymptotic stability of a cellular neural network with time delay feedback and zero control templates. Due to their sector restricted nonlinearities, stability of the neural networks is strongly connected to robust stability. With respect to this we shall use a quadratic Liapunov functional constructed via the technique due to V. L. Kharitonov for uncertain linear time delay systems, combined with an approach suggested by Malkin for systems with sector restricted nonlinearities.