Exponential Stability Analysis for Delayed Neural Networks via A Cubic Function Negative-Determination Lemma

This paper concerns with the exponential stability of delayed neural networks via Lyapunov-Krasovskii functional (LKF) method. Initially, an improved augmented delay-product-type LKF containing an additional double integral state is established, which introduces more delayed states and has less conservatism. In the LKF's derivative, the function has high order of delay due to the existence of exponent. Thus, in order to obtain tractable linear matrix inequalities, three state vectors are used to reduce the order of the function to cubic. Secondly, to achieve the negative-definiteness requirement, a negative-determination lemma for cubic functions with less conservatism is employed. Then, a less conservative delay-dependent stability criterion for neural networks with time-varying delays is established. Finally, the validity of the proposed delay-dependent stability criterion is illustrated by two numerical examples.