本文基於李亞普諾夫之穩定定理(Lyapunov Theorem)，針對某一類含有非匹配擾動及單輸入雙輸出之不確定非線性系統，提出一種順滑模態觀測器設計方法。首先提出具有調適機制的觀測器並設計順滑平面，使得觀測器能自動估測到擾動的上界，所以擾動的上界資訊不需要事先預知，還可以使系統中的第一個狀態誤差於有限時間內達到零。接著分析系統在有限時間內進入順滑平面之後，整個系統的狀態誤差皆能達到漸進穩定性能之要求。最後，本論文提供一個數值範例及一個實際裝置範例以驗證所提出觀測器的可行性。

Based on the Lyapunov stability theorem, a sliding mode observer is proposed in this thesis for a class of single-input-two-output uncertain nonlinear systems with mismatched disturbances. A sliding surface function is firstly designed for the proposed observer with adaptive mechanisms embedded, so that the upper bounds of perturbations are not required to be known in advance, and the first state estimation error is able to reach zero within a finite time. Secondly stability analysis is demonstrated to ensure that the rest of state estimation errors have the ability to achieve asymptotic stability. A numerical example and a practical example are illustrated for showing the feasibility of the proposed methodology.

Contents
Abstract i
List of Figures iii
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of Sliding Mode Observers 4
2.1 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 4
2.2 Design of the Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Stability Analysis of the Designed Observer . . . . . . . . . . . . . . . . 7
Chapter 3 Computer Simulations 33
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Practical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 4 Conclusions 52
References 53
Appendix A 57

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