Improved Robust Passivity Criteria for Delayed Neural Networks

This paper investigates the robust passivity problem for neural networks with uncertain system parameters and a time-varying delay. Based on Lyapunov stability theory, ensuring the negative definiteness for the derivatives of the developed Lyapunov-Krasovskii functional (LKF) is necessary in order to derive a passivity criterion. A negative condition on the cubic polynomial over a certain interval is developed in this paper, which introduces some slack matrices to obtain an advanced negative condition. Taking advantage of this condition, an augmented LKF with more system state and delay function information, including several augmented vectors and a single-integral-based term, is constructed. Then some improved passivity criteria for delayed neural networks are derived on top of the proposed LKF and the negative condition. Finally, the effectiveness and superiority of the obtained passivity criteria are validated on two numerical examples.