教學大綱表
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課程名稱 (中文) 線性系統
(英文) Linear Systems
開課單位 電機工程學系
課程代碼 E4630
授課教師 呂虹慶
學分數 3.0 必/選修 選修 開課年級 大四
先修科目或先備能力:線性代數, 訊號與系統
課程概述與目標:線性系统理論是控制工程學科的一門基本的理論性课程,本課程主要是藉由基本線性系統理論分析,了解模型化及建立數學方程式的重要性。
教科書 C. T. Chen, Linear System Theory and Design, 3rd Ed.
參考教材 R. D. Strum and D. E. Kirk, Contemporary Linear System
DeCarlo, Linear System.
課程大綱 學生學習目標 單元學習活動 學習成效評量 備註
單元主題 內容綱要
1 Introduction 1. Introduction
2. Overview
1. Introduction
2. Overview
  • 講授
  •  
    2 Mathematical Description of Systems 1. Linear Systems
    2. Linear Time-Invariant Systems
    1. Linear Systems
    2. Linear Time-Invariant Systems
  • 講授
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    3 Mathematical Description of Systems 1. Causality and lumpedness
    2. Linearization
    1. Causality and lumpedness
    2. Linearization
  • 講授
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    4 Linear Algebra 1. Matrix theory (Basis, Representation, and orthonormalization)
    2. Linear Algebraic Equations
    3. Similarity Transformation
    1. Matrix theory (Basis, Representation, and orthonormalization)
    2. Linear Algebraic Equations
    3. Similarity Transformation
  • 講授
  • 平時考
  •  
    5 Linear Algebra 1. Diagonal Form and Jordan Form
    2. Functions of a Square Matrix
    3. Lyapunov Equation
    1. Diagonal Form and Jordan Form
    2. Functions of a Square Matrix
    3. Lyapunov Equation
  • 講授
  • 作業
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    6 Linear Algebra 1. Quadratic Form and Positive Definiteness
    2. Singular-Value Decomposition
    3. Norms of Matrices
    1. Quadratic Form and Positive Definiteness
    2. Singular-Value Decomposition
    3. Norms of Matrices
  • 講授
  • 作業
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    7 State Space Solutions and Realizations 1. Solution of LTI State Equations
    2. Equivalent State Equation
    1. Solution of LTI State Equations
    2. Equivalent State Equation
  • 講授
  • 作業
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    8 State Space Solutions and Realizations Realizations Realizations
  • 講授
  • 平時考
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    9 State Space Solutions and Realizations 1. Solution of LTV State Equations
    2. Equivalent Time-Varying Equations
    1. Solution of LTV State Equations
    2. Equivalent Time-Varying Equations
  • 閱讀討論
  • 期中考
  • Mid-term Exam  
    10 Stability 1. Input-Output Stability of LTI Systems
    2. Internal Stability
    3. Lyapunov Theorem
    1. Input-Output Stability of LTI Systems
    2. Internal Stability
    3. Lyapunov Theorem
  • 講授
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    11 Controllability and Observability 1. Controllability
    2. Observability
    1. Controllability
    2. Observability
  • 講授
  • 作業
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    12 Controllability and Observability 1. Canonical Decomposition
    2. Conditions in Jordan-Form Equations
    1. Canonical Decomposition
    2. Conditions in Jordan-Form Equations
  • 講授
  • 平時考
  •  
    13 Minimal Realizations and Coprime Fractions 1. Implications of Coprimeness
    2. Computing Coprime Fractions
    1. Implications of Coprimeness
    2. Computing Coprime Fractions
  • 講授
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    14 Minimal Realizations and Coprime Fractions 1. Balanced Realization
    2. Minimal Realizations
    1. Balanced Realization
    2. Minimal Realizations
  • 講授
  • 作業
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    15 State Feedback and State Estimators 1. State Feedback
    2. Regulation and Tracking
    1. State Feedback
    2. Regulation and Tracking
  • 講授
  • 作業
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    16 State Feedback and State Estimators State Estimators State Estimators
  • 講授
  • 平時成績
  • 平時考
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    17 State Feedback and State Estimators Feedback From Estimated States Feedback From Estimated States
  • 講授
  • 學期成績
  • 作業
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    18 Pole placement pole placement pole placement
  • 閱讀討論
  • 期末考
  • Final Exam  

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    教材編選: ■ 自編教材 ■ 教科書作者提供
    評量方法: 期末考:30%   期中考:30%   其他評量:10%   平時考:10%   作業:20%  
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