Novel stability criteria for discrete‐time delayed neural networks via extended negative‐definiteness approaches of matrix‐valued quadratic function
Ke‐You Xie, Wenhu Chen, Li Jin, Chuan‐Ke Zhang, Yong He
Abstract
Abstract This article investigates the stability analysis of discrete‐time neural networks with time‐varying delays by the utilization of quadratic delay information. First, three extended negative‐definiteness lemmas for matrix‐valued quadratic function with different matrices injection are established. Second, a novel delay‐product‐type Lyapunov functional with the asymmetric summation is developed to relax the positive‐definiteness of functional. Then, the proposed negative definite approaches are utilized in combination with some typical summation inequalities to realize the construction of linear matrix inequalities. Based on these improved technologies, two delay‐dependent stability criteria with less conservatism and fewer computational burdens are derived. Finally, several numerical examples are presented to show the validity and superiority of the proposed methods.