LMI conditions for stability of neural networks with distributed delays

This paper presents new sufficient conditions for global asymptotic stability of neural networks with discrete and distributed delays. By using appropriate Lyapunov–Krasovskii functionals, we derive stability conditions in terms of linear matrix inequalities (LMIs). This is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Moreover, existing conditions are mostly based on certain diagonal dominance or M matrix conditions on weight matrices of the neural networks, which only make use of absolute values of the weights and ignore their sign, and hence are somewhat conservative. The LMI-based results obtained here can get rid of this disadvantage and give less conservative stability conditions. We illustrate this with numerical examples.