Complementary results on the stability bounds of singularly perturbed systems
Complementary results on the stability bounds of singularly perturbed systems
复制标题
DOI：
10.1109/tac.2004.837546
复制
发表时间：
2004-11
影响因子：
6.8
通讯作者：
L. Cao;H. Schwartz
中科院分区：
文献类型：
--
作者：
L. Cao;H. Schwartz
在这篇注记中，我们将提供一种新的系统方法来刻画和计算奇摄动线性系统的稳定界。该方法基于一个附加矩阵摄动问题的反馈系统表示。其思想是将稳定界问题转化为反馈系统的稳定性问题。这种方法允许在建立基本反馈系统时有多种选择，因此有可能以多种不同的方式来表征和计算稳定界。通过构造两种不同的反馈系统，基于反馈系统方法，得到了一些已有的和新的关于稳定界的结果。新的结果补充了现有的基于频域的稳定性判据，使频域技术在稳定界问题上更加适用和有用。算例表明，新的稳定性判据在确定稳定界方面是有效和有用的。
In this note, we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system. The approach is based on the feedback system representation of an additional matrix perturbation problem. The idea is to change the stability bound problem to the stability problem of an underlying feedback system. This approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways. By formulating two kinds of different feedback systems, some existing and new results on the stability bounds are derived based on the feedback system approach. The new results complement the existing frequency-domain based stability criteria and make the frequency-domain technique more applicable and useful to the stability bound problem. An example is provided to show the new stability criterion is effective and useful in determining the stability bound.