這篇論文將探討具有狀態相依雜訊和外部干擾下的離散隨機Takagi and Sugeno模糊模型，系統中狀態方程式的參數大小有界，但含有不確定性。首先，我們利用線性矩陣不等式理論去取得一般模糊狀態估測器穩定的充分條件。緊接著探討，當外部雜訊為未知機率模型的情況下，我們將用最惡劣功率放大率的觀點，藉由線性矩陣不等式理論，推導出最佳韌性 濾波器。最後，當外部雜訊為高斯白雜訊時，我們將用條件機率的方法來推導出最佳模糊卡門濾波器。証明從狀態估測的觀點來看，隨機T-S模糊系統的狀態估測可以被視為隨機時變線性系統的估測問題。

In this thesis, the state estimation problem for the stochastic T-S fuzzy model withstate-dependent noise on the system matrix and the output matrix has been attacked. First, we have derived sufficient conditions for a class of standard fuzzy state observer to ensure that the state estimation error is mean square bounded. The observer gain matrices in the fuzzy observer can be obtained by solving a linear matrix inequality (LMI).Then, the optimal H_infinity fuzzy filtering problem is considered to minimize the worst-case ratio of the power of state estimation error to that of the external noises. The optimal H_infinity observer gain matrices can be obtained by solving two linear matrix inequalities. To further improve estimation performance, we have studied the optimal Kalman fuzzy filtering problem with the known statistical information of the process noise and the measurement noise of the uncertain stochastic T-S fuzzy model. It is shown that the minimum-variance estimation for the uncertain stochastic T-S fuzzy model is actually a linear estimation problem from the viewpoint of conditional expectation. Actually, The structure of the developed optimal Kalman fuzzy filter also very resembles that of the conventional Kalman filter. Comparison of estimation performances of the developed three estimators is made via simulation study which verifies the optimal and robust performance of the optimal Kalman fuzzy filter.

1 Introduction 1 1.1 Survey of Related Literature . . . . . . . . . . . . . . . . . . . .1 1.2 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . .2 1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . .3 1.4 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 2 Preliminary Materials Of Conditional Probability . . . . . .5 3 State Estimation of Stochastic Fuzzy Systems . . . . . . . .10 3.1 The Stochastic T-S Fuzzy Model . . . . . . . . . . . . . . . . . . . . 10 3.2 A Class Of Standard State Estimators for Stochastic Fuzzy System . 12 3.3 Optimal H1 Filter For Stochastic Fuzzy System . . . . . . . . . . . . 23 3.4 Optimal Fuzzy Kalman Filter Under Gaussian Assumption . . . . . . 29 3.5 Simulation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5.1 Conventional State Observer Design . . . . . . . . . . . . . . . 39 3.5.2 Optimal H1 Filter Design . . . . . . . . . . . . . . . . . . . . 40 3.5.3 The Optimal Fuzzy Kalman Filter . . . . . . . . . . . . . . . 41 3.5.4 Comparison of Estimation Performance . . . . . . . . . . . . . 41 4 Conclusion and Discussion 46 A Appendix 48 A.1 PROOF OF LEMMA 2 . . . . . . . . . . . . . . . . . . . . . . . . . 48 A.2 PROOF OF LEMMA 5 . . . . . . . . . . . . . . . . . . . . . . . . . 50

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