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研究生: 王豪章
Wang, Hao-Zhang
論文名稱: 估算 $mu$-norm 之上界的一些數值方法
Numerical Algorithms for Estimating Upper Bounds of $mu-$norm
指導教授: 王辰樹
Wang, Chern-Shuh
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2004
畢業學年度: 92
語文別: 英文
論文頁數: 17
中文關鍵詞: 數值方法
外文關鍵詞: Numerical Algorithms, mu -norm
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  • 這篇文章提出了一些估計 $mu$-norm 上界的數值方法。 由一些文獻中可知,計算 $mu$-norm 及其下界為 NP-hard 的問題。 因此在本文中我們專注於 $mu$-norm 上界的估計。

    In this paper, some numerical algorithms for the
    computation of an upper bound of the $mu$-norm are proposed. Some
    literature have shown that the computations for $mu$-norm and its
    lower bound are NP-hard problems. Hence, in this paper, we
    concentrate on the computation of an upper bound of $mu$-norm.

    1. Introduction .............................. 03 2. LMI type Algorithms ....................... 05 2.1 Ellipsoid Algorithm ( Bisection Algorithm ) .............................................. 05 2.2 Iterative Interior Point Method .......... 06 2.3 Quasi-Newton type Algorithm .............. 10 3. Numerical Experiment ...................... 13 4. Concluding Remarks ........................ 16 References ................................... 17

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    [5] A. Packard, J. Doyle, The Complex Structure Singular Value, Automatica, vol.29, no.1, p72-p109,1993.

    [6] H. N. Huang, M. L. Jiang, $mu$-Synthesis
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    [7] W. W. Lin, P. H. Tang, Q. F. Xu, On the computation of the Optimal $H_{infty}$-norm for Two Feedback Problem.

    [8] O. Toker, H. $ddot{mbox{O}}$zbay. On the
    Complexity of Purely Complex $mu$ Computation and Relate Problems
    in Multidimensional Systems. IEEE TRANSACTIONS ON AUTOMATIC
    CONTROL, vol.43, no.3, p409-p414, March 1998.

    [9] C. T. Lawrence, A. L. Tits, P. Van Dooren, A fast algoithm for the computation of an upper bound on the $mu$-norm. C.T. Lawrence et al.,Automatica , vol.36, 2000, p449~p456.

    [10] K. Zhou, J.C. Doyle, and K. Glover. Robust and Optimal Control. Prentice Hall, Upper Saddle River, New Jersey.

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