時延與非時延濾波器穩定度分析比較; Stability Analysis and Comparison for Filters with Time Delay or No-Time Delay

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Title:	時延與非時延濾波器穩定度分析比較;Stability Analysis and Comparison for Filters with Time Delay or No-Time Delay
Authors:	羅吉昌
Contributors:	機械工程學系
Keywords:	H∞ 濾波;時延系統;Takagi-Sugeno 模糊模型;線性矩陣不等式 (LMI);H∞ filtering;Time delays;Takagi-Sugeno fuzzy model (T-S fuzzy model);Linear matrix inequality (LMI);電子電機工程類
Date:	2005-07-01
Issue Date:	2010-11-30 15:12:51 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	在本計畫中，我們將探討離散時間時延模糊系統的模糊濾波問題。其中模糊時延系統考慮的是具有多個時間延遲項及外來干擾（disturbance）的T-S 模糊架構，且特別針對延遲時間為固定的情況做討論。因應這種情況，我們採用一種特殊架構的濾波器，來解決上述濾波問題。在性能方面，分別考慮了H2、H∞及混合H2/H∞性能來分別討論。根據李亞普諾夫定理（Lyapunov theory），我們得以獲得可使原系統與濾波器之間之誤差系統（filtering error dynamic）穩定並同時分別達成H2、H∞及混合H2/H∞性能的三個充分條件。這三個條件都以線性矩陣不等式（LMI）的形式表示，因此可以現有的凸集合演算法（convex algorithms）求解之。最後，文末也將以舉例證明理論可行。此外，在研究過程發現，經由新變數的定義，離散時延系統可成功轉換為非時延系統，轉換方法的深入研究，及轉換前後的穩定度、解空間、、、等問題探討則用於申請計畫，指導學生完成。 In this proposal, we study H2 ,H∞ and mixed H2/H∞ filter design methodologies for a set of discrete-time Takagi-Sugeno fuzzy model with multiple time delays. And we focus on the time-fixed delay case where a filter of specific structure is considered to solve these filtering problems. Furthermore, a unified proof using Lyapunov theory is used to derive three sufficient conditions in the form of LMI. These conditions guarantee both stability and H2 , H ∞ and mixed H2/H∞ performance, respectively, for the filtering error dynamics. Lastly, an example demonstrates the mixed H2/H∞ filter design methodology. In the process of our study, a method transforming delay system into non-delay system is discovered. The differences between delay systems and non-delay systems are needed for further research in the aspects of stability and solvable regions that will be the focus of our proposal. 研究期間：9308 ~ 9407
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Departmant of Mechanical Engineering ] Research Project

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