Stability criterion for delayed neural networks via Wirtinger-based multiple integral inequality

This brief provides an alternative way to reduce the conservativeness of the stability criterion for neural networks (NNs) with time-varying delays. The core is that a series of multiple integral terms are considered as a part of the Lyapunov-Krasovskii functional (LKF). In order to estimate the multiple integral terms in the derivative of the LKF, a multiple integral inequality, named Wirtinger-based multiple integral inequality (WMII), is proposed. This inequality includes some recent related results as its special cases. Based on the multiple integral forms of LKF and the WMII, a novel delay dependent stability criterion for NNs with time-varying delays is derived. The effectiveness of the established stability criterion is verified by an open example.