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Abstract

In recent years, the concept of Lyapunov stability has received a remarkable attention in the field of neural networks. However the stability in Lagrange sense for neural networks has not been studied much. It is to be noticed that while Lyapunov stability refers to stability of the equilibrium point, Lagrange stability refers to the stability of the total system. In this paper, we study the global exponential stability in Lagrange sense for periodic neural networks with multiple time delays and more general activation functions including general bounded and sigmoidal type activation functions. By constructing suitable Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. We present a detailed estimation of global exponential attractive sets from the system parameters without any supposition on existence. We investigate whether the equilibrium point of the network system is globally exponentially stable by means of globally exponentially attractive sets. At the end, we give some numerical examples to validate our analytical findings. The results obtained are helpful in designing globally asymptotically stable cellular neural networks and reduce the search domain of optimization.