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研究生:郭岳承
研究生(外文):Yuen-Cheng Kuo
論文名稱:週期及二次矩陣束的特徵值反問題
論文名稱(外文):Inverse eigenvalue problems for periodic matrix pencil and quadratic pencil
指導教授:林文偉林文偉引用關係
指導教授(外文):Wen-Wei Lin
學位類別:博士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:80
中文關鍵詞:正則化反問題
外文關鍵詞:regularizationinverse problem
相關次數:
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  • 點閱點閱:96
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  • 下載下載:9
  • 收藏至我的研究室書目清單書目收藏:0
第一部分,我們想利用狀態和微分回饋控制把一個時變週期離散的系統正則化,在這部分我們找到一個可以正則化的充分條件,並利用構造方法證明在這充分條件之下可以構造出狀態和微分回饋控制矩陣,使的這週期閉迴路系統可以被正則化。另外也對於有限特徵值配置的反問題有一些結果。
第二部分,我們是對二次特徵值反問題加以探討,也就是說給定部份特徵值和特徵向量要反求二次 n 維矩陣對,在這部分主要分成兩種不同的類型,第一種類型是給定部份特徵值的個數是不大於 n 個,第二種類型是解決給定部份特徵值的個數是等於 n+1 個。這兩類問題主要都是利用構造的方法構造出二次矩陣對,但解決的技巧是全然不同的。
In Chapter 1, we consider the regularization problem for the linear time-varying
discrete-time periodic descriptor systems by derivative and proportional state feedback
controls. Sufficient conditions are given under which derivative and proportional
state feedback controls can be constructed so that the periodic closed-loop
systems are regular and of index at most one. The construction procedures used to
establish the theory are based on orthogonal and elementary matrix transformations
and can, therefore, be developed to a numerically efficient algorithm. The problem
of finite pole assignment of periodic descriptor systems is also studied.
In Chapter 2, the inverse eigenvalue problem of constructing real and symmetric
square matrices M,C and K of size n × n for the quadratic pencil Q(λ) = λ^2M +
λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is
considered. This chapter consists of two parts addressing two related but different
problems.
Contents
Chapter 1 Regularization of Discrete-Time Periodic Descriptor
Systems 1
1 Introduction 1
2 Preliminaries 5
3 Canonical Forms of {(E_j,A_j,B_j)} 15
4 Regularization of {(Ej,Aj,Bj)} 25
5 Pole Assignment of Periodic Descriptor Systems 36
6 Conclusion 37
Chapter 2 Inverse Quadratic eigenvalue problems 38
1 Introduction 38
2 Solving ISQEP 43
2.1 Recipe of Construction 44
2.2 Eigenstructure of Q(λ) 47
2.3 Numerical Experiment 54
3 Solving IMQEP 60
3.1 Real Linearly Dependent Eigenvector 61
3.2 Complex Linearly Dependent Eigenvector 64
3.3 Numerical Examples 69
4 Conclusion 74
References 75
References
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