課程名稱Course Title (中文) 線性系統 (英文) Linear Systems 開課單位Departments 電機工程學系 課程代碼Course No. E4630 授課教師Instructor 呂虹慶 學分數Credit 3.0 必/選修core required/optional 選修 開課年級Level 大四 先修科目或先備能力(Course Pre-requisites)：線性代數, 訊號與系統 課程概述與目標(Course Overview and Goals)：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(Textbook) C. T. Chen, Linear System Theory and Design, 3rd Ed. 參考教材(Reference) R. D. Strum and D. E. Kirk, Contemporary Linear System DeCarlo, Linear System.
 課程大綱 Syllabus 學生學習目標Learning Objectives 單元學習活動Learning Activities 學習成效評量Evaluation 備註Notes 序No. 單元主題Unit topic 內容綱要Content summary 1 Introduction 1. Introduction 2. Overview 1. Introduction 2. Overview 2 Mathematical Description of Systems 1. Linear Systems 2. Linear Time-Invariant Systems 1. Linear Systems 2. Linear Time-Invariant Systems 3 Mathematical Description of Systems 1. Causality and lumpedness 2. Linearization 1. Causality and lumpedness 2. Linearization 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 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 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 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 8 State Space Solutions and Realizations Realizations Realizations 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 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 11 Controllability and Observability 1. Controllability 2. Observability 1. Controllability 2. Observability 12 Controllability and Observability 1. Canonical Decomposition 2. Conditions in Jordan-Form Equations 1. Canonical Decomposition 2. Conditions in Jordan-Form Equations 13 Minimal Realizations and Coprime Fractions 1. Implications of Coprimeness 2. Computing Coprime Fractions 1. Implications of Coprimeness 2. Computing Coprime Fractions 14 Minimal Realizations and Coprime Fractions 1. Balanced Realization 2. Minimal Realizations 1. Balanced Realization 2. Minimal Realizations 15 State Feedback and State Estimators 1. State Feedback 2. Regulation and Tracking 1. State Feedback 2. Regulation and Tracking 16 State Feedback and State Estimators State Estimators State Estimators 17 State Feedback and State Estimators Feedback From Estimated States Feedback From Estimated States 18 Pole placement pole placement pole placement Final Exam

 序No. 實施期間Period 實施方式Content 教學說明Teaching instructions 彈性教學評量方式Evaluation 備註Notes 1 起:2024-01-01 迄:2024-01-05 1.同步遠距教學 Synchronous distance learning State Feedback and State Estimators: State Estimators 2 起:2024-01-08 迄:2024-01-12 1.同步遠距教學 Synchronous distance learning State Feedback and State Estimators: Feedback From Estimated States 作業 請於 2024/1/12 前於 Tronclass 繳交彈性教學週之作業

 教學要點概述： 1.自編教材 Handout by Instructor： ■ 1-1.簡報 Slids ■ 1-2.影音教材 Videos □ 1-3.教具 Teaching Aids □ 1-4.教科書 Textbook □ 1-5.其他 Other ■ 2.自編評量工具/量表 Educational Assessment □ 3.教科書作者提供 Textbook 成績考核 Performance Evaluation： 期末考：25%   期中考：25%   彈性教學：10%   平時考：20%   作業：20%   教學資源(Teaching Resources)： □ 教材電子檔(Soft Copy of the Handout or the Textbook) □ 課程網站(Website) 教學相關配合事項：教材電子檔講解為主, 黑板講解為輔. 扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php