Improved Stability criterion for Delay Neural Networks: High-order Matrix-valued Polynomial Approach

This paper presents a stability criterion for delayed neural networks system through a high-order matrix-valued polynomial approach. The augmented generalized Lyapunov-Krasovskii functionals (LKFs) are adopted to consider cross information about the delay state of the neural networks system. To approximate the upper bound of the quadratic integral terms in derivate of LKFs, the integral inequality based on free matrices is applied. In addition, zero equation which is obtained from the time delay assumption is added to LKF to reflect more information on the delay neural networks system. Two numerical examples showed that the proposed stability criterion guarantees the larger maximum admissible time delay bounds.