Numerous studies on various neural models have been reported with intensifying the development through successful applications in various fields that include image processing, signal processing, and artificial intelligence. However, these applications depend on the qualitative behaviours such as stability, convergence, periodic behavior, bifurcation and chaos. Among them stability analysis is most important as it is circuit phenomena for computational intelligent model. In this presentation is mainly concerned with the stability analysis of neural network model under time-delays. Through Lyapunov stability theory, different investigations such as stability criteria and synchronization criteria with various controls are handled with Lyapunov-Krasovskii functional and linear matrix inequality. Theoretical investigations are validated with numerical analysis.