奇攝動系統(tǒng)產生于小參數導致系統(tǒng)的剛性和系統(tǒng)階數的增加。此類系統(tǒng)具有多時標結構,使得系統(tǒng)更復雜。奇攝動模型最早用來處理此類系統(tǒng)。過去幾十年,奇攝動模型在控制領域迅猛發(fā)展。有許多關于連續(xù)和離散的奇攝動控制系統(tǒng)這方面的結果�；谄鏀z動理論的最近研究,本文研究離散奇攝動的魯棒穩(wěn)定,并提出某些新的結果�？偨Y本博士論文的如下主要結果。1.首先,研究了離散奇攝動系統(tǒng)的魯棒漸近穩(wěn)定。運用不動點定理和矩陣不等式技巧,給出孤立根存在的充分條件使得奇攝動系統(tǒng)是標準奇異攝動。進一步,利用兩時標分解方法,獲得快慢子系統(tǒng);基于快慢子系統(tǒng),利用組合方法證明了整個奇攝動系統(tǒng)是魯棒漸近穩(wěn)定的。2.第二個結果是研究不確定奇攝動系統(tǒng)的魯棒穩(wěn)定和魯棒鎮(zhèn)定問題。首先本文通過不動點原理和線性矩陣不等式,找出一個充分條件使得保證所考慮的奇攝動系統(tǒng)是標準奇攝動。于是原來的系統(tǒng)可分解為一個連續(xù)慢子系統(tǒng)和一個離散快子系統(tǒng)。因此基于兩時標分解技巧,給出一個線性矩陣不等式(LMIs)充分條件使得原系統(tǒng)是標準奇攝動系統(tǒng),同時它又是輸入到狀態(tài)穩(wěn)定(ISS)的。進一步,利用LMIs方法構造的狀態(tài)反饋控制器(具有參考輸入)使得相應的閉環(huán)系統(tǒng)仍然是I...

【文章頁數】：94 頁

【學位級別】：博士

【文章目錄】：
摘要
ABSTRACT
CHAPTER 1 Introduction
    1.1 Introduction of Singularly Perturbed Systems
    1.2 Historical Background
    1.3 Dissertation Organization
    1.4 Nomenclature and Notation
    1.5 Abbreviations
CHAPTER 2 Mathematical Preliminaries
    2.1 Stability
        2.1.1 Lyapunov Stability
        2.1.2 Input to State Stability(ISS)
        2.1.3 Local Input-to-State Stability
        2.1.4 Global Input-to-State Stability
    2.2 Input-to-State Stability Lyapunov Function
    2.3 Robust Control
    2.4 Linear Matrix Inequility
    2.5 Schur Complement Lemma
CHAPTER 3 Robust Asymptotic Stability of Discrete-Time Singularly Perturbed Systems
    3.1 Introduction:
    3.2 Problem Statement
    3.3 Robust asymptotic stability of discrete-time singularly perturbed system
        3.3.1 The Existence of an Isolated Root Analysis
        3.3.2 Robust Asymptotic Stability Analysis
    3.4 A Numerical Example
    3.5 Conclusion
CHAPTER 4 Robust Stability of Uncertain DiscreteTtime Singularly Perturbed System with Disturbance
    4.1 Introduction
    4.2 Problem Statement
    4.3 Input-to-State Stability of Discrete-Time Singularly Perturbed System
        4.3.1 The Existence of an Isolated Root Analysis
        4.3.2 Input-to-State Stability Analysis
        4.3.3 Input-to-State Stability of Closed-Loop System
    4.4 Numerical Examples
    4.5 Conclusion
CHAPTER 5 Roust H_∞ Control of Discrete-Time Singularly Perturbed System
    5.1 Introduction
    5.2 Problem Statement
    5.3 H_∞ Performance Analysis of Discrete-Time Singularly Perturbed System
    5.4 H_∞ Control of Discrete-Time Singularly Perturbed System
    5.5 Comparison with the Existing Results
    5.6 Numerical Examples
    5.7 Conclusion
CHAPTER 6 Conclusion and Future Work
    6.1 Conclusion
    6.2 Suggestions for Future Work
References
Pulications
Award
Acknowledgements
Vitae and Resume



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