本論文係探討n階適應性積分可變結構導數估測器之設計。文中所設計的導數估測器可視為現有的估測器之延伸，當輸入訊號是平滑且具n階微分的有界訊號時，這個新架構可以被直接當作n階的微分器使用。針對切換增益，我們使用適應性運算法則除去了需預知輸入訊號微分上界的要求。新設計的一階、二階以及n階架構的

This thesis is concerned with the designing of an nth order adaptive integral variable structure derivative estimator (AIVSDE). The proposed estimator's scheme is in fact a modified and extended version of the existing AIVSDE. The new proposed AIVSDE can be used as a direct nth differentiator for a smooth signal which has n continuous and bounded derivatives. The adaptive algorithm is utilized for the switching gain to remove the requirement for a priori knowledge about the upper bound of the derivative of the input signal. The stability of the redesigned first order, the second order, and the nth order derivative's estimation is guaranteed by the proposed scheme. An example is demonstrated for showing the applicability of the proposed AIVSDE.

Contents
Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation............................ 1
1.2 Brief Sketch of the Contents.................. 2
Chapter 2 Introduction to Background of the AIVS Derivative Estimator 4
2.1 Design of the First Order AIVS Derivative Estimator[1]..........4
Chapter 3 Design of the nth Order AIVSDE.........10
3.1 Design of the First Order AIVSDE.........10
3.2 Design of the second Order AIVSDE.........13
3.3 Design of the third Order AIVSDE.........17
Chapter 4 Simulations 23
Chapter 5 Conclusions 37
Bibliography 38

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