Improved Stability Criteria for Delayed Neural Networks via Time-Varying Free-Weighting Matrices and S-Procedure.

This brief investigates the stability of neural networks with time-varying delays. Novel stability conditions are derived by employing free-matrix-based inequality and introducing the variable-augmented-based free-weighting matrices in the estimation of the derivative of the Lyapunov-Krasovskii functionals (LKFs). Both techniques avoid the appearance of the nonlinear terms of the time-varying delay. Especially, the time-varying free-weighting matrices associated with the derivative of the delay and the time-varying S-Procedure related to the delay and its derivative are combined to improve the presented criteria. Finally, numerical examples are given to illustrate the benefits of the presented methods.