稳定反馈空间的拓扑结构
On the Topological Structure of Stable Feedback Space
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摘要: 本文讨论控制系统反馈空间的拓扑结构.首先讨论线性情况.然后,将其结果推广到非 线性的情况.赋予线性反馈集合以Rn×m拓扑(其中n为状态空间维数,m为输入维数),在这 个拓扑下研究完全能控系统稳定反馈集合的几何结构.文中证明了稳定反馈集合的拓扑结构 与具体系统无关.并且,对较小维数的系统(n≤5)给出了具体的拓扑结构.Abstract: The topological structure of feedback space for control system is discussed in this paper. Firstly, the linear case is considered. Then the results are generalized to nonlinear case. We define the Rn×m topology on the set consisting of linear state feedbacks (n is the dimension of state space, m is the dimension of output). Under this topology, the geometric structure of the set consisting of stable feedbacks is investigated. It is proved in the paper that the topology structure of the set consisting of stable feedbacks is independent of concrete system. Moreover, there gives the concrete topological structure for those systems with smaller dimension (n≤5).
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Key words:
- Stable feedback /
- topology /
- contractible /
- pathconnected
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