Stability Analysis of Delayed Recurrent Neural Networks via a Quadratic Matrix Convex Combination Approach

This brief addresses the stability analysis problem of a class of delayed recurrent neural networks (DRNNs). In previously published studies, the slope information of activation function (SIAF) is just reflected in three slope information matrices, i.e., the upper and lower boundary matrices and the maximum norm matrix. In practice, there are 2ⁿ possible combination cases on the slope information matrices. To exploit more information about SIAF, first, an activation function separation method is proposed to derive n slope-information-based uncertainties (SIBUs) containing SIAF; second, a quadratic matrix convex combination approach is proposed to dispose n SIBUs using 2ⁿ combination slope information matrices. Third, a stability criterion with less conservatism is established based on the proposed approach. Finally, two simulation examples are used to testify the validity of theoretical results.