奇攝動(dòng)系統(tǒng)產(chǎn)生于小參數(shù)導(dǎo)致系統(tǒng)的剛性和系統(tǒng)階數(shù)的增加。此類系統(tǒng)具有多時(shí)標(biāo)結(jié)構(gòu),使得系統(tǒng)更復(fù)雜。奇攝動(dòng)模型最早用來處理此類系統(tǒng)。過去幾十年,奇攝動(dòng)模型在控制領(lǐng)域迅猛發(fā)展。有許多關(guān)于連續(xù)和離散的奇攝動(dòng)控制系統(tǒng)這方面的結(jié)果。基于奇攝動(dòng)理論的最近研究,本文研究離散奇攝動(dòng)的魯棒穩(wěn)定,并提出某些新的結(jié)果。總結(jié)本博士論文的如下主要結(jié)果。1.首先,研究了離散奇攝動(dòng)系統(tǒng)的魯棒漸近穩(wěn)定。運(yùn)用不動(dòng)點(diǎn)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(dòng)系統(tǒng)是標(biāo)準(zhǔn)奇異攝動(dòng)。進(jìn)一步,利用兩時(shí)標(biāo)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(gè)奇攝動(dòng)系統(tǒng)是魯棒漸近穩(wěn)定的。2.第二個(gè)結(jié)果是研究不確定奇攝動(dòng)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(dòng)點(diǎn)原理和線性矩陣不等式,找出一個(gè)充分條件使得保證所考慮的奇攝動(dòng)系統(tǒng)是標(biāo)準(zhǔn)奇攝動(dòng)。于是原來的系統(tǒng)可分解為一個(gè)連續(xù)慢子系統(tǒng)和一個(gè)離散快子系統(tǒng)。因此基于兩時(shí)標(biāo)分解技巧,給出一個(gè)線性矩陣不等式(LMIs)充分條件使得原系統(tǒng)是標(biāo)準(zhǔn)奇攝動(dòng)系統(tǒng),同時(shí)它又是輸入到狀態(tài)穩(wěn)定(ISS)的。進(jìn)一步,利用LMIs方法構(gòu)造的狀態(tài)反饋控制器(具有參考輸入)使得相應(yīng)的閉環(huán)系統(tǒng)仍然是I...

【文章頁數(shù)】：94 頁

【學(xué)位級(jí)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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