Global Exponential Stability of Impulsive Delayed Neural Networks on Time Scales Based on Convex Combination Method
研究了时标上脉冲延迟神经网络的全局指数稳定性，通过构造脉冲依赖的李雅普诺夫泛函和时标不等式技术，得到了代数与线性矩阵不等式条件，适用于离散、连续及混合时间神经网络，并用四个数值例子验证了有效性。
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.