时滞系统的完全稳定性研究综述

Survey on complete stability study for time-delay systems

时滞系统的完全稳定性问题是控制领域中的一个基础理论问题,长期以来受到了人们的关注.然而,该问题非常复杂,人们往往存在一些不正确的理解,目前国内外尚未见到专门关于这一问题的综述性文献.对此,从基础知识、现有方法回顾、技术难点、求解思路等方面对时滞系统完全稳定性问题做一个全面、直观的介绍.最后,介绍一种最近提出的分析方法—–频域扫描框架.在该框架下,时滞系统完全稳定性问题能够得到完整的解决.

The complete stability of time-delay systems is a fundamental academic problem in the control field, which has attracted wide attention for a long time. However, people may tend to have some incorrect understanding of the complete stability. In the open literature, no dedicated survey paper has been reported so far concerning this topic. In this survey paper, the complete stability of time-delay systems is reviewed in terms of preliminaries, existing results, technical difficulties, and the idea of solution. Finally, a recently-established tool, the new frequency-sweeping framework, is introduced. Within this framework, the complete stability is systematically solved for the first time.