臺灣博碩士論文加值系統

本論文係研究不確定線性奇異系統(uncertain linear singular system)
之強健性問題。由於奇異系統之不確定性(uncertainties)，不但會影響
其穩定性(stability)，也會影響系統所特有的正則性(regularity)及脈
衝免疫性(impulse-immunity)，後兩者的問題在標準狀態空間系統(
standard state-space system)中並不會發生，所以研究奇異系統的強健
性問題比標準狀態空間系統複雜許多。 利用線性分式轉換(Linear
Fractional Transformation, LFT)，可表示不同型式的不確定奇異系統
，並結合守護映射(guardian map)的觀念與結構化奇異值 m 的理論，有
系統地解決強健性問題。針對不同型式的不確定奇異系統，求出含不確定
性參數系統所能容忍的最大變動範圍和充要條件，以確保系統的正則性、
脈衝免疫性和穩定性。 除了強健穩定性之外，強健D-穩定性問題也在研
究範疇中，以確保系 統的特徵值被安置在某一特定穩定區域內，使系統
不但保有穩定性，更保證所需的強健性能。本研究架構可以成功地應用到
連續時間與離散時間系統。在論文中，吾人將舉例說明各種研究架構之可
行性。

The robustness of uncertain linear singular systems is
investigated in this dissertation. It is known that when the
robust stability problem is investigated, the regularity and
impulse-immunity must be considered simultaneously. The latter
two problems do not arise in standard state-space systems.
Therefore, the robustness problem of linear singular systems is
more complicated than that in standard state-space systems.
Based on LFT descriptions used to characterize the various kinds
of uncertain linear singular systems, the guardian map and the
structured singular value are also involved to deal with the
robustness analysis for both continuous-time and discrete-time
systems. Some methodical approaches are provided to derive the
maximal bounds of parametric uncertainties or the sufficient and
necessary conditions in which the properties of regularity,
impulse-immunity and stability are robustly preserved for
various kinds of uncertain linear singular systems. In
addition, the D-stability robustness problem is also
investigated to guarantee stability and required performance of
the systems. The LFT approach provides a unified framework for
both continuous-time and discrete-time uncertain linear singular
systems. Several illustrative examples are given to show the
feasibility of the proposed approaches.

Cover
Chinese Abstract
English Abstract
Acknowledgment
Contents
List of Figures
Notation and Abbreviations
Chapter 1 Introduction
1.1 Motivation
1.2 Related Works
1.3 Contribution and Organization
Chapter 2 Mathematical Preliminaries
2.1 Linear Fractional Transformations: LFTs
2.2 Kronecker Operations
2.3 Guardian Maps
2.4 Structured Singular Value:μ
Chapter 3 Robustness Analysis of Generalized Interval Systems
3.1 Problem Formulation
3.2 Stability Robustness of Continuous-Time Cases
3.3 Stability Robustness of Discrete-Time Cases
3.4 Illustrative Examples
3.5 Summary
Chapter 4 Robustness Analysis of Singular Systems with Linearly prametric Uncertainties
4.1 Problem Formulation
4.2 Main Results of Continuous-Time Cases
4.3 Main Results of Discrete-Time Cases
4.4 Illustrative Examples
4.5 Summary
Chapter 5 Robustness Analysis of Uncertain Singular Systems with Output Feedback Control
5.1 Problem Formulation
5.2 Uncertain Singular Systems With LFT Descriptions
5.3 Robustness Analysis
5.4 Illustrative Examples
5.5 Summary
Chapter 6 D-Stability Robustness of Singular Systems with A One-Parameter Family of Perturbations: Frequency-Domain Approach
6.1 Problem Formulation
6.1.1 Uncertain Singular Systems with LFT Descriptions
6.1.2 Robustness Intervals
6.2 D-Stability Robustness of Continuous-Time Cases
6.3 D-Stability Robustness of Discrete-Time Cases
6.4 Illustrative Examples
6.5 Summary
Chapter 7 D-Stability Robustness of Singular Systems with A One-Parameter Family of Perturbations: Time-Domain Approach
7.1 Problem Formulation
7.2 New Formulas for Kronecker Operations of LFTs
7.3 D-Stability Robustness of Continuous-Time Systems
7.4 D-Stability Robustness of Discrete-Time Systems
7.5 Disconnected D-Stability Robustness
7.6 Illustrative Examples
7.7 Summary
Chapter 8 Conclusions and Further Work
8.1 Conclusions
8.2 Further Work
Bibliography
Publication List
Vita