最大結構奇異值上界計算的數值演算一直在μ-合成控制問題扮演關鍵角色, 如文內所示, 最大結構奇異值的計算是NP-hard 的問題, 因此, 我們會專注在計算最大結構奇異值的上界之研究。一種牛頓法型態的演算法已發展, 一些和演算相關的理論結果也已被探究。
此文中, 我們也可以把此問題轉換成線性矩陣不等式(linear matrix inequality ,簡稱LMI) 來研討, 並學習如何使用MATLAB 內建的LMI Control Toolbox 數值求解LMI, 由數值結果的比較可知, 牛頓法的效能優於LMI Control Toolbox, 雖然LMI Control Toolbox 已被廣泛應用於這類問題, 最後我們就LMI 在廣義特徵值
問題上編纂簡易的使用手冊, 以供來者參考。

Numerical algorithms are proposed for computing an upper bound of the largest structured singular value which always plays a key role to a μ-synthesis control problem are proposed. Literatures have shown that the computations
for the largest structured singular value is an NP-hard problem. We hence concentrate on the study for computing an upper bound of the largest structured singular value in this dissertation.
In this dissertation, we firstly transfer the problem into the linear matrix inequality (abbreviated as LMI), and further use LMI Control Toolbox built in MATLAB to solve LMI. We compare numerical results using LMI Control
Toolbox with that using the Newton-type method which is recently developed. The comparison shows that the Newton’s method is more efficient than LMI Control Toolbox. We also appendix a for solving a generalized eigenvalue
problem in LMI form by using LMI control Toolbox.

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