Global Exponential Stability of Impulsive Delayed Neural Networks on Time Scales Based on Convex Combination Method

The published stability criteria for impulsive neural networks are scale-free on time line, which is only appropriate for discrete or continuous ones. The issue of global exponential stability for impulsive delayed neural networks on time scales is analyzed by employing the convex combination method in this article. Several algebraic and linear matrix inequality conditions are proved by constructing impulse-dependent Lyapunov functionals and using timescale inequality techniques. Unlike the published works, impulsive control strategies can be designed by utilizing our theoretical results to stabilize delayed neural networks on time scales if they are unstable before introducing impulses. Sufficient criteria for global exponential stability in this article are derived based on the timescale theory, and they are applicable to discrete-time impulsive neural networks, their continuous-time analogues, and neural networks whose states are discrete at one time and continuous at another time. Four numerical examples are offered to demonstrate the effectiveness and superiority of our new theoretical results in the end.

Automated summary

This article analyzes the issue of global exponential stability for impulsive delayed neural networks on time scales by constructing impulse-dependent Lyapunov functionals and using timescale inequality techniques. The theoretical results derived from the timescale theory can be used to design impulsive control strategies to stabilize previously unstable delayed neural networks. The effectiveness and superiority of these results are demonstrated through numerical examples.