Stability Analysis of Recurrent Neural Networks With Time-Varying Delay by Flexible Terminal Interpolation Method

This brief studies the stability problem of recurrent neural networks with time-varying delay. Based on one tunable parameter
$\alpha $
, a flexible terminal interpolation method is proposed to change the interval with fixed terminals as
$2^{k+1}-3$
ones with flexible terminals. Associated with the flexible subintervals, a novel Lyapunov–Krasovskii functional with more delay information is constructed. In order to estimate the Lyapunov–Krasovskii functional, a quadratic reciprocally convex inequality is proposed, which covers some existing ones as its special cases. Based on these ingredients, a new stability criterion is derived in the form of linear matrix inequalities. A comprehensive comparison of results is given to illustrate the newly proposed stability criterion.