A review on evolution of Lyapunov-Krasovskii function in stability analysis of recurrent neural networks with single time-varying delay

In the stability analysis of recurrent neural networks, one of the tasks is to reduce the conservativeness of the stability criterion. Along this routine, there are two ways to be considered. One is how to construct the Lyapunov-Krasovskii functional (LKF), and the other is how to use mathematical skills to estimate the derivatives of the LKF. The purpose of this paper is to present a brief review on the evolution on the construction of LKF for recurrent neural networks with single time-varying delay. By summarizing the observation, one can find the core elements in the construction of LKF. Moreover, one can find the evolution history on the delay-partitioning and its applications in the construction of LKF.