Stability Analysis for Delayed Neural Networks Based on A Sufficient and Necessary Condition on Polynomial Inequalities

This paper presents an improved stability condition for neural networks with a time-varying delay. In the derivative of Lyapunov-Krasovskii functional (LKF), the non-convex polynomials in the time-varying delay may appear and result in the difficulties for making the derivative of LKF negative-definite. This paper utilizes a negativity-determination method reported recently to handle the non-convex time-varying delay polynomials. The employed method presents necessary and sufficient negativity condition for polynomials. The application of this negativity-determination method to neural networks with a time-varying delay leads to a less conservative stability criterion, which is illustrated with an example.