Some novel results for DNNs via relaxed Lyapunov functionals

The focus of this paper was to explore the stability issues associated with delayed neural networks (DNNs). We introduced a novel approach that departs from the existing methods of using quadratic functions to determine the negative definite of the Lyapunov-Krasovskii functional's (LKFs) derivative $ \dot{V}(t) $. Instead, we proposed a new method that utilizes the conditions of positive definite quadratic function to establish the positive definiteness of LKFs. Based on this approach, we constructed a novel the relaxed LKF that contains delay information. In addition, some combinations of inequalities were extended and used to reduce the conservatism of the results obtained. The criteria for achieving delay-dependent asymptotic stability were subsequently presented in the framework of linear matrix inequalities (LMIs). Finally, a numerical example confirmed the effectiveness of the theoretical result.