| 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 | Nonlinear Models and Nonlinear Phenomena |
Pendulum Equation, Tunnel-Diode Circuit |
推導非線性系統方程式 |
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Matlab program demonstration |
| 2 | Nonlinear Models and Nonlinear Phenomena |
Mass-Spring System, Negative-Resistance Oscillator, Artificial Neural Network, Adaptive Control |
推導非線性系統方程式 |
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| 3 | Second-Order Systems |
Qualitative Behavior of Linear Systems |
相平面的建立及軌跡繪製 |
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Matlab program demonstration |
| 4 | Second-Order Systems |
Multiple Equilibria, Qualitative Behavior Near Equilibrium Points |
平衡點的定義及建立 |
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| 5 | Second-Order Systems |
Limit Cycles, Numerical Construction of Phase Portraits, Existence of Periodic Orbits, Bifurcation |
各種非線性系統的定義及比較 |
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| 6 | Fundamental Properties |
Existence and Uniqueness |
非線性系統有解的存在性及唯一性 |
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Matlab program demonstration |
| 7 | Fundamental Properties |
Continuous Dependence on Initial Conditions and Parameters |
初始位置的影響及設定 |
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| 8 | Lyapunov Stability |
Autonomous Systems |
自發性系統的定義及特性 |
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| 9 | Lyapunov Stability |
The Invariance Principle |
非線性系統的不變性定義 |
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| 10 | Lyapunov Stability |
Linear Systems and Linearization |
推導非線性系統與線性系統間的轉換 |
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Matlab program demonstration |
| 11 | Lyapunov Stability |
Comparison Functions |
推導非線性系統的比較函數 |
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| 12 | Lyapunov Stability |
Nonautonomous Systems |
非自主性非線性系統定義及特性 |
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| 13 | Lyapunov Stability |
Linear Time-Varying Systems and. Linearization |
線性時變系統特姓解析 |
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Matlab program demonstration |
| 14 | Lyapunov Stability |
Converse Theorems |
系統的反向推論定理 |
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| 15 | Lyapunov Stability |
Boundedness and Ultimate Boundedness |
非線性系統的有界定義及特性 |
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| 16 | Lyapunov Stability |
Input-to-State Stability |
非線性系統輸入輸出穩定定義及分析 |
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Matlab program demonstration |
| 17 | Lyapunov Stability |
Input-to-State Stability |
非線性系統輸入輸出穩定分析 |
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| 18 | Lyapunov Stability |
Input-to-State Stability |
非線性系統輸入輸出穩定分析 |
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