| 均方稳定的多维AR系统的一个性质 |
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| 引用本文： | 曹显兵,黄先开.均方稳定的多维AR系统的一个性质[J].北京工商大学学报(自然科学版),2002,20(3):59-62. |
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| 作者姓名： | 曹显兵 黄先开 |
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| 作者单位： | 北京工商大学,基础部,北京,100037 |
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| 基金项目： | 国家自然科学基金;2000-60075019; |
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| 摘 要： | ARX系统的随机适应控制常导致其闭环稳态 AR系统的均方稳定性 .在噪声满足一定的矩条件下 ,证明了若多维 AR系统 A( z) yk=wk 在下列意义下均方稳定 :lim supn→∞1n ∑nk=1‖yk‖ 2 <∞ a.s.则 det A( z)不可能有爆炸的根 ,即 det A( z)的零点全在单位圆上或圆外 .
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| 关 键 词： | AR系统 均方稳定 鞅差序列 |
| 文章编号： | 1671-1513(2002)03-0059-04 |
| 修稿时间： | 2002年5月21日 |
PROPERTY OF MULTIDIMENSIONAL AR SYSTEMS BEING STABLE IN MEAN SQUARE |
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| CAO Xian bing,HUANG Xian kai.PROPERTY OF MULTIDIMENSIONAL AR SYSTEMS BEING STABLE IN MEAN SQUARE[J].Journal of Beijing Technology and Business University:Natural Science Edition,2002,20(3):59-62. |
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| Authors: | CAO Xian bing HUANG Xian kai |
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| Abstract: | Stochastic adaptive stabilization of ARX system usually leads to the resulting system being stable in the mean square. Imposing certain conditions on the noise, this paper proves that multidimensional AR system A(z)y k=w k being stable in the mean square, by which it is meant that the long run average of the squared output is bounded: lim sup n→∞1n ∑nk=1‖ y k‖ 2<∞ , hasn't any explosive roots, i.e., all roots of det A(z) are on or outside the unit circle. |
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| Keywords: | AR system stability in mean square martingale difference sequence |
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