Decomposition of Third-Order Linear Time-Varying Systems into Its Second- and First-Order Commutative Pairs
Decomposition of Third-Order Linear Time-Varying Systems into Its Second- and First-Order Commutative Pairs
复制标题
三阶线性时变系统分解为其二阶和一阶交换对
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Yakar
中科院分区：
文献类型：
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作者：
M. E. Koksal;A. Yakar
分解是合成许多物理系统的常用工具。它也用于分析大规模系统，然后被称为撕裂和重建。另一方面，级联连接系统的交换性获得了极大的兴趣，其可能的好处已在文献中指出。本文研究了任意三阶线性时变系统可分解为参数也是显式表示的一阶和二阶系统可交换对的充要条件。此外，在非零初始条件的情况下，导出的额外的要求。本文重点介绍了实现任何三阶线性时变系统作为一个系列（级联）连接的第一和第二阶子系统的直接公式。这种串联连接是可交换的，因此它独立于连接中的子系统的顺序。因此，方便的顺序可以决定考虑系统的整体性能时，考虑灵敏度，干扰和鲁棒性的影响。实现包括瞬态响应以及稳态响应。
Decomposition is a common tool for the synthesis of many physical systems. It is also used for analyzing large-scale systems which are then known as tearing and reconstruction. On the other hand, commutativity of cascade-connected systems has gained a great deal of interest, and its possible benefits have been pointed out on the literature. In this paper, the necessary and sufficient conditions for decomposition of any third-order linear time-varying system as a commutative pair of first- and second-order systems of which parameters are also explicitly expressed, are investigated. Further, additional requirements in case of nonzero initial conditions are derived. This paper highlights the direct formulas for realization of any third-order linear time-varying systems as a series (cascade) connection of first- and second-order subsystems. This series connection is commutative so that it is independent from the sequence of subsystems in the connection. Hence, the convenient sequence can be decided by considering the overall performance of the system when the sensitivity, disturbance, and robustness effects are considered. Realization covers transient responses as well as steady-state responses.