随机脉冲时刻下微分系统的稳定性
Stabilization of Differential Systems with Random Impulsive Effect
DOI: 10.12677/AAM.2014.32013, PDF, HTML, 下载: 2,957  浏览: 9,990  国家自然科学基金支持
作者: 韩文博, 高彩霞：内蒙古大学数学科学学院，呼和浩特
关键词: 脉冲微分系统；P阶指数稳定性；随机过程；Lyapunov直接法；充分条件；Impulsive Differential System； P-Moment Exponential Stability； Stochastic Process； Lyapunov’s Direct Method； Sufficient Conditions
摘要: 本文研究了当脉冲时刻是随机变量时，脉冲微分系统的稳定性。因为在随机脉冲时刻的影响下，脉冲微分方程的解为随机过程，这与传统的确定性脉冲时刻的微分方程解的性质相差甚远。本文便研究随机脉冲的发生是如何影响系统稳定性的，并给出使系统P阶指数稳定的充分条件。
Abstract: This paper studies the stability of impulsive differential systems when the pulses happen in the random time. Under the influence of random pulses, the solutions of impulsive differential equations become the stochastic processes, so the solutions are far different from the deterministic impulsive differential equations’. In this paper, we study how the random pulses affect the stability of the systems, and then the sufficient condition on P-moment stability is established.
文章引用：韩文博, 高彩霞. 随机脉冲时刻下微分系统的稳定性[J]. 应用数学进展, 2014, 3(2): 85-90. http://dx.doi.org/10.12677/AAM.2014.32013

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