<p>This study presents a variable-augmented free-weighting matrix framework for analyzing the exponential stability of time-delayed neural network systems. Significant emphasis has been placed on the reduced conservatism and simplicity of contemporary stability criteria in the systematic evaluation of global exponential stability. Time-varying delayed neural networks are addressed using an enhanced free-weighting matrix method with variable augmentation to effectively resolve this issue. This approach reduces superfluous decision variables and averts the formation of higher-order delay terms. This leads to the development of new-brand global exponential stability conditions in the form of linear matrix inequalities, offering improved computational efficiency and reduced conservatism. The practicality and effectiveness of the proposed approach are finally demonstrated through two numerical examples.</p>