本論文基於李亞普諾夫理論(Lyapunov Theorem)，針對兩種具有匹配式非線性干擾的多變數廣義系統分別提出兩種可變結構控制器。為了解決穩定化的問題，首先提出積分式可變結構控制器；接下來再提出的是參考模型可變結構控制器，以解決狀態追蹤的問題。兩種控制方法皆可保證受控系統的軌跡自初始時間即存在於所設計的順滑面內，使得系統之解的存在與唯一性，無脈衝性以及穩定性皆可達成。最後舉出兩個數值模擬來驗證控制方法的可行性。

Based on the Lyapunov stability theorem, two different variable structure controllers are proposed in this thesis for two different classes of multi-variable descriptor systems subject to matched nonlinear perturbations. The integral variable structure controller is proposed first for solving the stabilization problems, and model reference variable structure controller is the second for solving the state tracking problems. Both proposed control schemes can guarantee the trajectories of the controlled systems to lie in the sliding surface from initial time, so that the properties of regularity, impulse free, and stability can be obtained. Two numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Contents
Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation............................ 1
1.2 BriefSketchoftheContents.................. 4
Chapter 2 Introduction to Descriptor Systems Theory 5
2.1 SolvabilityofDescriptorSystems ............... 5
2.2 Coordinate Transformations and Basic System Theorems . . 7
2.3 ConceptsofControllability................... 10
2.4 ConceptsofObservability ................... 12
Chapter 3 Design of Variable Structure Controllers for Sta-bilization
15
3.1 SystemDescriptionsandAssumptions ............ 15
3.2 DesignofSlidingSurface.................... 17
3.3 DesignofControllersandStabilityAnalysis ......... 24
ii.3.4 SummaryofDesignProcedure ................ 28
Chapter 4 Design of Model Reference Variable Structure
Controllers 30
4.1 SystemDescriptionsandAssumptions ............ 30
4.2 DesignofSlidingSurface.................... 33
4.3 Design of Model Reference Variable Structure Controllers . . 35
4.4 SummaryofDesignProcedure ................ 38
Chapter 5 Simulations 39
Chapter 6 Conclusions 53
References 55

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