不确定采样数据系统的稳定性分析
Stability Analysis of Uncertain Sampled-Data Systems
DOI: 10.12677/PM.2014.43012, PDF,    国家自然科学基金支持
作者: 贾 荣, 高彩霞：内蒙古大学数学科学学院，呼和浩特
关键词: 脉冲系统；重置设计；采样数据系统；稳定性；Lyapunov函数；多面体嵌入；Impulsive System； Reset Design； Sampled-Data System； Stability； Lyapunov Functions； Polytopic Embedding
摘要: 本文主要研究了具反馈控制的线性时不变脉冲系统的稳定性问题。在过去的理论中认为，脉冲是造成系统不稳定的重要因素。在这里，我们将脉冲系统看作特殊的重置系统，继而得到，在适当的脉冲作用下，系统不但能保持原来的稳定性，甚至可以使一个原来不稳定的系统变得稳定。本文以经典的Lyapunov方法为基础，以线性矩阵不等式LMI为表达形式，给出使系统平衡点全局一致指数稳定的充分必要条件。并以此为基础，对不稳定的微分控制系统，给出使系统指数稳定的脉冲重置的设计方法及重置矩阵的形式。文章最后将结果运用到不确定的LTI采样数据系统中，并给出算例。
Abstract: This paper deals with the stability of linear time-invariant impulsive system with feedback control. The pulses, at some time in the past, were the important factor causing system instability. Here, we first regard the impulsive system as a special reset system, then we analyze the stability of sampled-data system, and design reset matrices such that the uncertain sampled-data system is stable. Based on the classical Lyapunov method and linear matrix inequality LMI form, the necessary and sufficient conditions for stability are given. At last, we apply the results to the uncertain LTI sampled-data systems and illustrate a numerical example.
文章引用：贾荣, 高彩霞. 不确定采样数据系统的稳定性分析[J]. 理论数学, 2014, 4(3): 75-83. https://dx.doi.org/10.12677/PM.2014.43012

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