离散奇摄动系统的相关研究
发布时间：2024-02-17 21:43
奇摄动系统产生于小参数导致系统的刚性和系统阶数的增加。此类系统具有多时标结构,使得系统更复杂。奇摄动模型最早用来处理此类系统。过去几十年,奇摄动模型在控制领域迅猛发展。有许多关于连续和离散的奇摄动控制系统这方面的结果。基于奇摄动理论的最近研究,本文研究离散奇摄动的鲁棒稳定,并提出某些新的结果。总结本博士论文的如下主要结果。1.首先,研究了离散奇摄动系统的鲁棒渐近稳定。运用不动点定理和矩阵不等式技巧,给出孤立根存在的充分条件使得奇摄动系统是标准奇异摄动。进一步,利用两时标分解方法,获得快慢子系统;基于快慢子系统,利用组合方法证明了整个奇摄动系统是鲁棒渐近稳定的。2.第二个结果是研究不确定奇摄动系统的鲁棒稳定和鲁棒镇定问题。首先本文通过不动点原理和线性矩阵不等式,找出一个充分条件使得保证所考虑的奇摄动系统是标准奇摄动。于是原来的系统可分解为一个连续慢子系统和一个离散快子系统。因此基于两时标分解技巧,给出一个线性矩阵不等式(LMIs)充分条件使得原系统是标准奇摄动系统,同时它又是输入到状态稳定(ISS)的。进一步,利用LMIs方法构造的状态反馈控制器(具有参考输入)使得相应的闭环系统仍然是I...
【文章页数】：94 页
【学位级别】：博士
【文章目录】：
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
本文编号：3901369
【文章页数】：94 页
【学位级别】：博士
【文章目录】：
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
本文编号：3901369
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