本論文基於李亞普諾夫之穩定性定理(Lyapunov Theorem)，針對具有匹配式與非匹配式擾動系統，且含有不可量測狀態，提出一個適應性可變結構觀測器及控制器處理系統校準問題。首先根據系統設計順滑模態觀測器，用來估測不可量測狀態，下一步設計控制器使得系統軌跡在有限時間內進入順滑面，當系統進入順滑模態之後有效抑制非匹配擾動對系統的影響，且可以達到漸進穩定性能之要求。為了抑制非匹配擾動對系統的影響，將調適機制運用在順滑面及控制器的設計中，致使控制器自動調整未知擾動的上界，所以擾動的上界資訊就不需事先知道，還可使受控系統於有限時間內達到迫近模態。最後，本論文提供一個數值範例及實際裝置的範例以檢驗所提出控制器的可行性。

Based on the Lyapunov stability theorem, an adaptive variable structure observer and a controller are proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems with unmeasurable states to solve regulation and tracking problems. In order to estimate the unmeasurable states, a design methodology of variable structure observers is presented first. Then the controller is designed so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. Some adaptive mechanisms are embedded in the sliding surface function and sliding mode controllers, so that not only the mismatched perturbations are suppressed effectively during the sliding mode, but also the information of upper bounds of some perturbations are not required. When the controlled system is the sliding mode, the stability or asymptotical stability is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed design technique.

Abstract ...................................i
List of Figures .......................iv
1 Introduction ........................1
1.1 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . 3
2 Design of Robust Variable Structure Observers and Controllers for
Mismatched Uncertain Systems to Achieve Asymptotical Stability ...............................5
2.1 System Descriptions and Problem Formulations . . . . . . . . . 5
2.2 Design of the Robust Observers and Controllers . . . . . . . . . 8
2.3 Stability Analysis of Estimation Errors . . . . . . . . . . . . . . 12
2.4 Analysis of Overall System’s Stability . . . . . . . . . . . . . . 20
3 Design of model reference Adaptive sliding mode tracking controllers
and observer for mismatched uncertain systems ...26
4 Computer simulations ..........................................33
4.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Practical Example . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 TrackingExample . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Conclusions and FutureWorks ...........................56
References .............................................................56

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