| Лурье问题的降维解法 |
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| 引用本文： | 肖淑贤. Лурье问题的降维解法[J]. 华中科技大学学报(自然科学版), 1992, 0(1) |
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| 作者姓名： | 肖淑贤 |
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| 作者单位： | 华中理工大学数学系 |
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| 摘 要： | 本文研究了题的降维解法.证明当c属于一个确定的线性变换的k维不变子空间时,原系统的绝对稳定性与一k维系统的绝对稳定性相同.文中特别证明了当c属于这个变换的一维或二维不变子空间时,猜测成立,并给出了一类系统绝对稳定的充要性代数条件.
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| 关 键 词： | 绝对稳定性 不变子空间 Aйзерман猜测 降维解法 等价系统 |
A Dimension Reducing Method for Solving Lurie''''s Problem |
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| Xiao Shuxian. A Dimension Reducing Method for Solving Lurie''''s Problem[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 1992, 0(1) |
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| Authors: | Xiao Shuxian |
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| Affiliation: | Xiao Shuxian |
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| Abstract: | A dimension reducing method for solving Lurie( )'s problem is studied, it is proved that the absolute stability of a nonlinear control system is equivalent to that of another system with a lower dimension when the feedback vector c belongs to the invariant subspace of a definite linear transform. It is also pointed out that the Aizerman conjecture is true if c belongs to one or two dimensional invariant subspace of the linear transform. Some applications and examples are given. |
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| Keywords: | absolute stability invariant subspace Aizerman conjecture dimension reducing method equivalence system |
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