In this dissertation, we address the robust stabilization design problem for nonlinear stochastic distributed parameter systems (NSDPSs) with random external disturbances and measurement noises in the spatio-temporal domain. A fuzzy stochastic distributed parameter system is proposed to approximate the NSDPS based on fuzzy interpolation approach. Then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic distributed parameter system via a semi-discretization finite difference scheme. Based on this model, a robust fuzzy estimator-based stabilization controller is proposed to stabilize the NSDPS. Furthermore, the robust stochastic $H_\infty$ stabilization design is proposed to attenuate the effects of random external disturbances and measurement noise in the spatio-temporal domain from the area energy point of view, and the LMI technique is applied to solve the control gains and estimator gains of the controller via a systematic control design procedure. Finally, a simulation example is given to illustrate the design procedure and to confirm the performance of the proposed robust fuzzy estimator-based stabilization design for the NSDPSs.

在本論文中，我們探討非線性隨機分佈參數系統的隨機穩定化問題，和有外部擾動和量測雜訊影響下的非線性隨機分佈參數系統的強健性 $H_\infty$ 穩定化問題。我們更針對外部的擾動和量測雜訊是在空間位置分佈的情況下來探討其穩定化的控制器設計。模糊方法被廣泛的應用於非線性系統的近似。因此，我們利用模糊內插法，提出一個模糊隨機分佈參數系統來近似原本的非線性隨機分佈參數系統。然後使用半離散化的有限差分法，我們發展一個模糊隨機的狀態空間模型，來取代模糊隨機分佈參數系統。模糊隨機的狀態空間模型是被證明可以近似原本的非線性隨機分佈參數系統。因此，基於這個模型，一個強健模糊估測器結合穩定化控制器是被提出來控制非線性隨機分佈參數系統使其穩定。控制器使其系統穩定的條件是被證明只要符合一個矩陣不等式即可被保證。進一步地，強健性 $H_\infty$ 控制設計法則是被提出來消除外部干擾和量測雜訊對系統輸出的影響。因為控制器增益及估測器增益互相偶和的問題，所以設計條件是一個雙線性的矩陣不等式。為了有系統的解決設計的問題，我們簡化BMI的問題成LMI的問題，並使用 LMI 技巧來求解控制器增益和估測器增益。最後，為了呈現設計的性能及方法的實用性，我們給一個神經系統的例子來說明控制器設計的流程，並驗證設計方法的效能。

Contents
中文摘要 . . . . . . . . . . . . . . iv
英文摘要 . . . . . . . . . . . . . . v
誌謝 . . . . . . . . . . . . . . . vi
Contents . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . ix
1 Introduction . . . . . . . . . . 1
2 Preliminaries and Problem Formulation . . 8
2.1 Stochastic Stability of NSDPSs . . . 10
2.2 Stochastic $H_\infty$ Stabilization Control for NSDPSs . . . 12
3 System Representation by Fuzzy Spatial State Space Model . . . . 15
4 Robust Stabilization Design for Nonlinear Stochastic Distributed Parameter Systems . . . 26
4.1 Robust Fuzzy Estimator-based Stabilization Control Design . . . 27
4.2 LMI Approach for Solving Robust Stochastic $H_\infty$ Stabilization Control Problem . . . 43
5 Simulation Examples . . . 52
6 Conclusion . . . . . . . 66
Bibliography . . . . . . . 68
Publications List . . . . . . 78

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