An LMI approach to global asymptotic stability of the delayed Cohen–Grossberg neural network via nonsmooth analysis

In this paper, a linear matrix inequality (LMI) to global asymptotic stability of the delayed Cohen-Grossberg neural network is investigated by means of nonsmooth analysis. Several new sufficient conditions are presented to ascertain the uniqueness of the equilibrium point and the global asymptotic stability of the neural network. It is noted that the results herein require neither the smoothness of the behaved function, or the activation function nor the boundedness of the activation function. In addition, from theoretical analysis, it is found that the condition for ensuring the global asymptotic stability of the neural network also implies the uniqueness of equilibrium. The obtained results improve many earlier ones and are easy to apply. Some simulation results are shown to substantiate the theoretical results.

An analysis of exponential stability of delayed neural networks with time varying delays

This paper derives a new sufficient condition for the exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a Lyapunov-Krasovskii functional and using Linear Matrix Inequality (LMI) approach. This result establishes a relation between the delay time and the parameters of the network. The result is also compared with the most recent result derived in the literature.

Global dissipativity of continuous-time recurrent neural networks with time delay

This paper addresses the global dissipativity of a general class of continuous-time recurrent neural networks. First, the concepts of global dissipation and global exponential dissipation are defined and elaborated. Next, the sets of global dissipativity and global exponentially dissipativity are characterized using the parameters of recurrent neural network models. In particular, it is shown that the Hopfield network and cellular neural networks with or without time delays are dissipative systems.

Global exponential stability of continuous-time interval neural networks

This paper addresses global robust stability of a class of continuous-time interval neural networks that contain time-invariant uncertain parameters with their values being unknown but bounded in given compact sets. We first introduce the concept of diagonally constrained interval neural networks and present a necessary and sufficient condition for global exponential stability of these interval neural networks irregardless of any bounds of non-diagonal uncertain parameters in connection weight matrices. Then we extend the robust stability result to general interval neural networks by giving a sufficient condition. Simulation results illustrate the characteristics of the main results.