多重輸入時滯系統之Hankel範數計算

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Title:	多重輸入時滯系統之Hankel範數計算
Other Titles:	Hankel Norm Computation for Linear Time-Invariant Systems with Multiple Input Delays
Authors:	林秋君 Lin, Chiu-Chun
Contributors:	黃皇男 Huang, Huang-Nan 東海大學數學系
Keywords:	時滯系統;穩定性;Hankel運算子;奇異值;直饋型時滯 delay systems;stability;Hankel operator;singular value;feedthrough delay
Date:	2001
Issue Date:	2011-05-25T09:46:27Z (UTC)
Abstract:	本篇論文的主要目的在探討穩定線性非時變且具備多重輸入時滯系統之Hankel範數。首先，採用穩定等價的觀念來分析時滯系統之穩定性。繼而，針對直饋型輸入時滯系統推導其Hankel運算子與其伴隨運算子，並討論此種運算子之緊緻性。最後，本文分別從誘導範數的定義及運算子奇異值之最大值即為其範數的觀念來計算此種運算子之範數。研究結果顯示:範數之值為包含延遲時間與時滯個數效應的特定矩陣之行列式的最大零點，文中並舉例說明Hankel範數的計算過程。 In this thesis, we are concerned with the computation of the Hankel norm for stable linear time-invariant systems with multiple input delays. First of all, the stability of delay systems is analyzed by using the concept of stability equivalence. Next, the Hankel operator of linear systems with feedthrough-type input delays and its adjoint are constructed. The compactness of this operator is then examined. Afterward, the norm computation of Hankel operator is studied in two different approaches: one is based on definition of induced operator norm, and the other is based on the fact that the value of norm is equal to the largest singular value of the operator. The result shows that the Hankel norm is just the largest root of an algebraic equation which actually is the determinant of certain complicated matrix including the effect of time-length and number of delays. Some illustrative examples are presented.
Appears in Collections:	[Department of Applied Mathematics] Theses and Dissertations

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