Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays

In this paper, the global exponential stability in Lagrange sense related to inertial neural networks with time-varying delay is investigated. Firstly, by constructing a proper variable substitution, the original system is transformed into the first order differential system. Next, some succinct criteria for the ultimate boundedness and global exponential attractive set are derived via the Lyapunov function method, inequality techniques and analytical method. Meanwhile, the detailed estimations for the global exponential attractive set are established. Finally, the effectiveness of theoretical results has been illustrated via two numerical examples.