Stability in delayed Cohen–Grossberg neural networks: LMI optimization approach

In this paper, stability problems are further discussed for a class of delayed Cohen–Grossberg neural networks. On the basis of the linear matrix inequality (LMI) optimization approach, and also the Lyapunov–Krasovskii functional method combined with the Halanay inequality technique, several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system. The proposed results are less restrictive than those given in the earlier literature, and are easier to verify in practice. In addition, four examples and their numerical simulations are given; two of them are used to demonstrate the effectiveness of the proposed results, and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold.