Synchronization of Discrete-Time Inertial Neural Networks Using the General Theory of Solutions of Linear Difference Equations

This paper investigates the quasi-synchronization (QS) problem for drive-response discrete-time delayed inertial neural networks (DTDINNS). Unlike existing studies that mainly rely on classical stability theorems, linear matrix inequality (LMI) methods, and matrix measure approaches (MMA), this work establishes three innovative quasi-synchronization criteria for DTDINNS by adopting the solution formula of second-order linear difference equations (SOLDES), infinite series summation techniques, and the solution formula of first-order linear difference equation group (Lemma 6). To the best of our knowledge, this study is the first attempt to introduce the general solution theory of second-order linear difference equations and infinite series summation methods to analyze the synchronization behavior of neural networks (NNS). The proposed framework offers a novel theoretical tool for the synchronization analysis of discrete-time delayed neural networks (DTDNNS), which bears important theoretical significance for relevant research fields.