This paper revisits the issue of stability analysis of neural networks subjected to time-varying delays. A novel approach, termed a compound-matrix-based integral inequality (CPBII), which accounts for delay derivatives using two adjustable parameters, is introduced. By appropriately adjusting these parameters, the CPBII efficiently incorporates coupling information along with delay derivatives within integral inequalities. By using CPBII, a novel stability criterion is established for neural networks with time-varying delays. The effectiveness of this approach is demonstrated through a numerical illustration.

This paper explored the topic of extended dissipativity analysis for Markovian jump neural networks (MJNNs) that were influenced by time-varying delays. A distinctive Lyapunov functional, distinguished by a non-zero delay-product types, was presented. This was achieved by combining a Wirtinger-based double integral inequality with a flexible matrix set. This novel methodology addressed the limitations of the slack matrices found in earlier research. As a result, a fresh condition for extended dissipativity in MJNNs was formulated, utilizing an exponential type reciprocally convex inequality in conjunction with the newly introduced nonzero delay-product types. A numerical example was included to demonstrate the effectiveness of the proposed methodology.