一类无界区域上脉冲泛函微分方程的稳定性分析

对一类无界区域上脉冲泛函微分方程零解的指数稳定性进行研究。利用Fourier变换的方法推导出系统的解，再利用不等式放缩技巧对线性系统的Cauchy矩阵进行估计，最后由建立的积分不等式和假设的条件，给出非线性系统零解全局指数稳定性的一个充分条件。在非线性系统满足所给出的假设条件之下，零解是全局指数稳定的。研究结果推广了现有文献中的相关工作。

Stability Analysis of a Class of Impulsive Functional Differential Equations in Unbounded Domains

The exponential stability of zero solutions of a class of impulsive functional differential equations in an unbounded region is studied. The solution of the system is derived by using the Fourier transform method, and the Cauchy matrix of the linear system is estimated by using the inequality reduction technique. Finally, a sufficient condition for the global exponential stability of the zero solution of the nonlinear system is given by the established differential inequalities and the assumed conditions. Under the assumption that the nonlinear system satisfies the given conditions, the zero solution is globally exponentially stable. The results of this study extend the related works in the existing literature.