Global Exponential Stability Criteria for Proportional Delay High-Order Neural Networks: A Hyper-Exponential Stability Technique

Abstract

A new method is presented for stability analysis of proportional delay high-order neural networks. The network model is first transformed into a system with a constant time delay and unbounded time-varying coefficients, and then it is proven that the former is globally exponentially stable if and only if the laster is globally hyper-exponentially stable. The global hyper-exponential stability criteria of the laster are investigated by employing the generalized Halanay inequality and constructing a novel Lyapunov function that can avoid the computation of upper-right derivative. From which, the global exponential stability criteria of the former are derived. To illustrate the advantages of this proposed method, numerical simulation examples are given. Compared with the existing results, the contributions of this paper lie in: (i) An Lyapunov function different from ones in literature is constructed; (ii) The derived global exponential stability criteria possess simple forms, which are easy to verify; and (iii) The concept of hyper-exponential stability is proposed. The proposed method is also available to multi-proportional delay neural networks.