切換性多模組的方法已廣泛應用於線性時變系統的估測，最佳的估測法因為計算量隨時間成指數增加，所已有很多簡化，但效能仍不錯的估測器提出。應用範圍如飛行器追蹤、手機定位等。
對於線性系統中存有時變的參數，第二章提出以設定若干個子系統，以代表此切換系統的時變性。類似於前一章的方法，可對每一子系統設計一濾波器，並由每一子系統的相似度值為權重，合併起來為最後的估測值。應用的範圍如時變autoregressive model的估測。
Takagi-Sugeno模糊模型用來近似非線性系統，而濾波器亦可基於建立的模糊模型來做設計。但較少論文有關非系性時變系統的探討。對於時變的非線性系統，首先定義數個子系統，然後對個別子系統建立一模糊模型。基於此對於此模糊模型，可設計一模糊濾波器。最後，由每一子系統的相似度值為權重，合併起來為最後的估測值。
結合可切換性多模組與Takagi-Sugeno模糊模型這兩種方式，本文提出一個可切換性的模糊濾波器來估測系統狀態。為達到抑制雜訊及準確估測的效果，可切換性的模糊濾波器的設計要同時滿足H2及H∞準則，即在限制住雜訊對估測誤差的放大效應下，要設計濾波器使估測誤差最小。設計的限制條件可以轉成線性矩陣不等式(LMI)，並藉由一些最佳化方法，可以設計出濾波器。
最後，用電腦程式模擬來跟切換性extended Kalman filter (EKF)做比較。結果顯示，當存在不明干擾的情形下，H2/H∞準則所設計的濾波器有較大的強健性。第一個非線性時變系統的近似誤差比較小，但有不明的雜訊，所以，本文提出的切換性模糊H2/H∞濾波器跟switching extended Kalman filter比較起來，有較好的強健性。第二個非線性時變系統的近似誤差比較大，且有不明的雜訊，所以，switching extended Kalman filter的準確度大為降低，而，本文提出的切換性模糊H2/H∞濾波器仍具有較好的強健性。

The problem of state estimation for nonlinear stochastic systems subject to time-varying parameter or time-varying structure is considered. Switching multiple-modeling approach has been used to deal with linear systems with time-varying parameters or structures. On the other hand, Takagi-Sugeno (T-S) fuzzy modeling method is usually adopted to approximate the nonlinear time-invariant systems, but not suitable for nonlinear time-varying systems. Combining the switching multiple-modeling approach and T-S fuzzy modeling method, a fuzzy filter, realized using switching T-S fuzzy model, is proposed for the state estimation of the nonlinear time-varying stochastic systems. In order to mitigate the model approximation error and external disturbance in the systems, the proposed H2/H∞ switching fuzzy filter minimizes the upper bound of the H2-norm of estimation error system under the constraint that the H∞-norm (i.e., the worst-case effect of disturbance on estimation error) is less than a prescribed value. The conditions for the existence of such robust filter are provided in terms of linear matrix inequalities (LMIs), allowing the use of standard convex optimization procedures to solve the proposed H2/H∞ filtering problem for nonlinear time-varying systems. Finally, numerical simulations are provided to illustrate the design procedure and to confirm the performance of the proposed robust filter.

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