Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis-II

Following our recent approach of nonsmooth analysis, we report a new set of sufficient conditions and its implications for the global asymptotic stability of delayed cellular neural networks (DCNN). The new conditions not only unify a string of previous stability results, but also yield strict improvement over them by allowing the symmetric part of the feedback matrix positive definite, hence enlarging the application domain of DCNNs. Advantages of the new results over existing ones are illustrated with examples. We also compare our results with those related results obtained via LMI approach.

I. Introduction

Since its introduction by Chua and Yang [8], [9], the cellular neural network (CNN) has found a wide range of applications in many areas such as signal processing, pattern recognition, and moving image processing, to name a few. In the implementation of CNNs in those applications, it is sometimes necessary to introduce delays in the signals transmitted among cells [7]. This is how the delayed cellular neural network (DCNN) comes [25], [26]. The level of reliability of DCNNs depends on the global uniqueness of the equilibrium point as well as its asymptotic stability. Due to this reason, many papers are dedicated to the study of stability issue of DCNNs, see [1], [3], [4]–[6], [10], [13], [14], [18]–[21], [23], [27], [28], and references therein. It turns out that the stability analysis for DCNNs is much more difficult than for conventional CNNs.