Stability Analysis of Neural Networks with Time-Varying Delays via a Novel Generalized Integral Inequality Based on Free Matrices

This paper concerns the stability problem of neural networks with time-varying delay through the Lyapunov-Krasovskii (L-K) functional method. Appropriate L-K functionals were constructed with an augmented vector of state vector and its derivative term. A novel generalized integral inequality based on free matrices is utilized to estimate the tight upper bound of single integral terms of the L-K functional derivative term. Besides, zero equalities between state vector and delayed state vector are introduced to reduce conservatism of the stability criterion. To verify the superiority of the proposed method, two well-known examples are given.