离散时间系统零动态的研究现状和未来挑战

Current development and future challenges for zero dynamics of discrete-time systems

在数字控制系统的分析与设计中,零动态是一个被广泛关注的重要概念,近年来取得了诸多新的理论与方法进展.本文首先描述了离散时间系统零动态理论的研究背景和研究意义,同时简要介绍了离散时间系统零动态理论所涉及到的3个相关问题,如:信号的采样与重建、连续时间系统的等价离散时间系统模型以及在离散连续时间系统过程中所需要的工具(q算子和δ算子).其次,立足现有文献,针对离散零动态的特点,从线性离散时间系统和非线性离散时间系统两个方面全面而深入地介绍了近年来离散零动态研究工作的进展.最后分析了零动态在数字控制系统分析与设计中的局限性以及出现的挑战性课题,并指明未来工作的研究方向.

Zero dynamics has been broadly concerned in the analysis and design of digital control systems, about which a number of novel methods and algorithms have been developed recently. We give a description about the research back- ground and the significance of the zero dynamics theory for discrete-time systems, and briefly introduce several related issues of the discrete system zero dynamics theory, such as the signal sampling and reconstruction, discrete-time modeling of continuous-time systems, as well as the tools for discretization, i.e. q-operator and J-operator. According to the current literature, we categorize comprehensively the current development of the discretization zero dynamics in linear and nonlin- ear discrete-time systems. Finally, restrictions and challenging problems of zero dynamics in computer-controlled systems are put forward to readers, showing the future research directions in this field.