论构造可控性判据问题。1 .循环不变子空间

IF 0.3 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya Pub Date : 2023-01-01 DOI:10.21638/11701/spbu10.2023.213

Elizaveta A. Kalinina, A. M. Kamachkin, N. Stepenko, G. Tamasyan

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引用次数: 0

摘要

线性系统的卡尔曼可控性矩阵的秩取决于由输入矩阵的列生成的状态矩阵的不变循环子空间的基。详细研究了状态矩阵的约当形式和标量控制的情况。证明了循环子空间的维数是由输入矩阵列的坐标块的第一个非零元素的索引数决定的。这些子空间的基的形成完全公开。在此基础上，构建了构造控制系统的空间基础。

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On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces

The rank of the Kalman’s controllability matrix of linear systems depends on the bases of the invariant cyclic subspaces of the state matrix generated by the columns of the input matrix. The case of the Jordan form of the state matrix and scalar control is studied in detail. It is shown that the dimension of cyclic subspaces is determined by the index numbers of the first non-zero elements of the coordinate blocks of the columns of the input matrix. The formation of the bases of these subspaces is completely disclosed. Based on this, the basis of the space of a constructive control system is constructed.

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来源期刊

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.30

自引率

50.00%

发文量

期刊介绍： The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.