Controllability of systems described by convolutional or delay-differential equations
Controllability of systems described by convolutional or delay-differential equations
复制标题
由卷积或时滞微分方程描述的系统的可控性
DOI：
10.1109/cdc.2001.980236
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
S. Zampieri
中科院分区：
文献类型：
--
作者：
P. Vettori;S. Zampieri
本文研究了用时滞微分和更一般的卷积方程描述的线性定常无穷维系统的能控性。本文讨论了Willems的行为方法（1989，1993）和Fliess的模块理论方法（1992）中针对此类系统引入的各种可控性概念。谱可控性的一个表征，扩展的结果是已知的差分或微分方程。两个最重要的贡献，这两种方法，即存在的图像表示和平坦度，进行了比较。最后，它表明，一个定理，其中国家的谱能控性和存在的图像表示的等价性，成立的一类时滞微分系统，包括系统的状态空间形式。然而，这个结果对于一般的延迟微分或卷积系统是错误的，如一个例子所示。
In this paper controllability properties of linear time-invariant infinite dimensional systems described by delay-differential and by more general convolutional equations are considered. Various controllability notions which have been introduced for this class of systems in Willems' behavioral approach (1989, 1993) and in Fliess' module theoretic approach (1992), are here discussed. A characterization of spectral controllability is given, extending results that are known to hold for difference or differential equations. Two of the most important contribution of these two approaches, i.e. existence of an image representation and flatness, are compared. Finally, it is shown that a theorem, which states the equivalence of spectral controllability and the existence of an image representation, holds true for a class of delay-differential systems, including systems in state-space form. However, this result is false for generic delay-differential or convolutional systems, as an example shows.