New Analysis Method for Global Exponential Stability of Discrete-Time High-Order Neural Networks with Time-Varying Delays: in Lagrange Sense and in Lyapunov Sense

In this article, the global exponential stability and convergence domain analysis of high-order neural networks are investigated. First, a new method is proffered to find the stability criterion for delayed HONNs in Lagrange sense, and the exponential convergence domain for delayed HONNs is obtained. Meanwhile, some new criterion of global exponential stability (GES) for the zero equilibrium in Lyapunov sense can be derived. The novelty of this paper lies in that the rigorous stability and convergence analysis does not construct Lyapunov-Krasovskii functional, as well as the obtained criteria is global and essentially just verify whether a vector is non-negative. Finally, two numerical examples exhibit the validity of the results.