# 臺灣博碩士論文加值系統

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 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-varyingdiscrete-time periodic descriptor systems by derivative and proportional state feedbackcontrols. Sufficient conditions are given under which derivative and proportionalstate feedback controls can be constructed so that the periodic closed-loopsystems are regular and of index at most one. The construction procedures used toestablish the theory are based on orthogonal and elementary matrix transformationsand can, therefore, be developed to a numerically efficient algorithm. The problemof finite pole assignment of periodic descriptor systems is also studied.In Chapter 2, the inverse eigenvalue problem of constructing real and symmetricsquare 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 isconsidered. This chapter consists of two parts addressing two related but differentproblems.
 ContentsChapter 1 Regularization of Discrete-Time Periodic DescriptorSystems 11 Introduction 12 Preliminaries 53 Canonical Forms of {(E_j,A_j,B_j)} 154 Regularization of {(Ej,Aj,Bj)} 255 Pole Assignment of Periodic Descriptor Systems 366 Conclusion 37Chapter 2 Inverse Quadratic eigenvalue problems 381 Introduction 382 Solving ISQEP 432.1 Recipe of Construction 442.2 Eigenstructure of Q(λ) 472.3 Numerical Experiment 543 Solving IMQEP 603.1 Real Linearly Dependent Eigenvector 613.2 Complex Linearly Dependent Eigenvector 643.3 Numerical Examples 694 Conclusion 74References 75
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 1 多種玻色愛因斯坦凝聚現象之數值研究 2 Structuredbackwarderrorofpolynomialeigenvalueproblem 3 非線性矩陣方程之保結構算法的收斂性分析 4 弦方程在混合邊界條件下的反問題 5 二次特徵值的反問題 6 渾沌密碼與時空擾動之渾沌密碼流 7 一些邊界值含eigenparameter的向量型Sturm-Liouville方程式固有值問題的研究 8 OnCouplingStrengthofCoupledMapLattices 9 一類保結構阿洛迪方法求解二次特徵值問題 10 幾個有關於Sturm-Liouville方程式的固有值問題之研究 11 週期離散系統之分析 12 非拋物型有效質量近似二維連續薛丁格方程特徵值問題 13 延遲反饋之量子井雷射二極體的渾沌同步技術應用在光學數位通訊 14 Some eigenvalue problems related to the nonhomogeneous potential equation 15 Ontheexistenceofpositivesolutionsforcertainnonlinearequations

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