本文基於李亞諾夫之穩定定理(Lyapunov Theorem)，針對含有某一類高增益觀測器之不確定非線性系統，提出一種修正過的分析及設計方法。首先將對某類誤差系統，在前兩個狀態變數可以間接量測得的前提下進行穩定性分析。此種修正過的分析方法之優點是即使事先無法預測雜訊分佈函數之上界，仍能證明觀測誤差可以保證漸近穩定。下一步將針對含有未知上界干擾之系統在雜訊分佈函數可量測到的前提下重新設計觀測器。由於在觀測器中應用了適應機制，干擾之上界不需要預先知道。還可使受控誤差系統於有限時間內達到迫近模態。當系統進入順滑面後，即可保證系統漸近穩定。最後，本文將提供一個數值範例及一個實際應用，以驗證所提出觀測器的可行性。

Based on the Lyapunov stability theorem, a modified stability analysis as well as a modified observer is proposed in this thesis for a class of uncertain nonlinear systems with an existent high gain observer. By assuming that the first two state variables are indirectly measurable, reanalyzing the stability of the error dynamics is presented first. The advantage of this modified analytic method is that the upper bound of the disturbance distribution functions is not required to be known in advance, and the asymptotic stability is still guaranteed. Next, based on this existent observer, a slightly modified observer is presented for systems with disturbances whose upper bound is unknown. An adaptive mechanism is embedded in the proposed observer, so that the upper bound of perturbations is not required to be known beforehand. The resultant dynamics of estimation errors can be driven into the sliding surface in a finite time, and guarantee asymptotic stability. A numerical example and a practical example are given to demonstrate the feasibility of the proposed observer.

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 Stability Analysis of an Existent Sliding Mode Observers
for Disturbed Systems 4
2.1 System Descriptions and Problem Formulations . . . . . . . . . 4
2.2 Stability Analysis of an Existent Observer . . . . . . . . . . . . 6
2.3 Redesign of Sliding Mode Observer . . . . . . . . . . . . . . . 15
Chapter 3 Computer Simulations 21
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Practical Example . . . . . . . . . . . . . . . . . . . . . . . . . 24
Chapter 4 Conclusions 36
References 37

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