广义循环系统的特性分析

Character Analysis for Singular Circulant Systems

本文将正常循环系统推广为广义循环大系统,并利用矩阵理论,集中分析了这类大系统的一些重要性质及其分散固定模的特征。结果表明,Nn阶的广义循环大系统的性质如稳定性、能控性、能观性、固定模的存在性等,均可由一些低阶系统的相应性质来描述。并且广义循环大系统的有穷固定模可通过低阶系统的不可控不可观模态求得,从而避免了因系统的高维性带来的计算困难。本文的结论为进一步研究这类系统提供了理论基础。

In this paper, regular circulant systems are generalized to singular circulant systems. And via matrix theories, some important characters and fixed modes of such systems are mainly analyzed. It is shown that the characters, such as stability, controllability, observability, the existence of decentralized fixed modes, of this kind of large-scale systems can be exactly described by the corresponding properties of some lower-order models. And it is shown that the set of the finite fixed modes of such a system is equal to the union of the sets of uncontrollable and unobservable modes of some lower-order models such that the calculation difficulty due to the high dimension is avoided. The results in this paper provide the theory foundation to further study such systems.