Improved integral inequalities for stability analysis of delayed neural networks

This paper is concerned with the exponential stability of delayed neural networks. Combined the Legendre polynomials with free-weighting matrices technique, an improved free-matrix-based single integral inequality is given, which includes the general single integral inequality and the free-matrix-based single integral inequality as special cases. Furthermore, a free-matrix-based double integral inequality which improves the existing results is derived. As applications of these novel free-matrix-based integral inequalities, several exponential stability criteria with less conservatism for the delayed neural networks are obtained. The effectiveness of our main results is illustrated by three numerical examples from the literatures.