Pole Placement via the Periodic Schur Decomposition
Pole Placement via the Periodic Schur Decomposition
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通过周期性 Schur 分解进行极点放置
DOI：
10.23919/acc.1993.4793135
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
P. Van Dooren
中科院分区：
文献类型：
--
作者：
J. Sreedhar;P. Van Dooren
提出了一种利用线性周期状态反馈进行线性周期离散时间系统特征值配置的新方法。该方法采用了基于么正变换的可靠数值技术。本质上，它通过最近的隐式特征分解算法计算开环单调矩阵的Schur形式，并按顺序移动其特征值。给定开环系统的完全可达性，我们证明了可以用这种方式将任意一组特征值赋给闭环系统的单调矩阵。在较弱的完全可控性假设下，这种方法可以把所有的特征值都放在原点，从而解决所谓的无差拍控制问题。该算法很容易扩展到更一般的情况，例如当系统方程以描述符的形式给出时。
We present a new method for eigenvalue assignment in linear periodic discrete-time systems through the use of linear periodic state feedback. The proposed method uses reliable numerical techniques based on unitary transformations. In essence, it computes the Schur form of the open-loop monodromy matrix via a recent implicit eigen-decomposition algorithm, and shifts its eigenvalues sequentially. Given complete reachability of the open-loop system, we show that we can assign an arbitrary set of eigenvalues to the closed-loop monodromy matrix in this manner. Under the weaker assumption of complete control-lability, this method can be used to place all eigenvalues at the origin, thus solving the so-called deadbeat control problem. The algorithm readily extends to more general situations, such as when the system equation is given in descriptor form.