平面控制系统的线性对称性
On Linear Symmetry of Plane Control Systems
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摘要: 本文讨论了二维非线性系统在线性群作用下的对称性,及GL(2,R)的所有连通子群.换 言之,本文研究了控制系统的一切可能的线性对称性.文中给出各种情况下的充分必要条件, 并且对各类线性对称系统的构造给出完整的描述,从而显示了大量对称控制系统的存在性.Abstract: In this paper, we consider the symmetry of two dimensional control systems under linear groups. All connected Lie subgroups of GL(2,R)have been discussed, i.e., all possible linear symmetry of control systems are under investigation. Necessary and sufficient conditions are obtained for each case. The structures of all kinds of symmetric systems are presented, showing that there are plenty of symmetric control systems.
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Key words:
- Symmetry /
- general linear group /
- Lie algebra
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