随机系统的输入-状态稳定性与异步切换
发布时间：2024-03-10 18:17
随机系统是指系统的输入、输出和扰动有随机因素,或者系统本身有一些不确定性.众所周知,随机系统在科学、经济、物理、控制等领域具有广泛地应用.世界上许多学者都致力于研究随机系统的各种性质.特别地,稳定性和控制理论一直是有趣和重要的课题,因为他们能够描述随机系统的显著特征.切换系统作为一类混合系统,由一系列的子系统和控制系统间交换的交换信号构成.另一方面,在实际系统中不可避免地会遇到扰动,这意味着随机模型更适用于描述实际系统.以上综合考虑形成了一种新的模型-切换随机系统.如果系统的切换与控制器切换保持一致,叫做同步交换.而异步交换是相反的,是由于开关信号的检测延迟引起的,导致各子系统设计的控制器周期不匹配.因此,对切换随机系统的研究是非常重要并具有挑战意义的.除此以外,我们还考虑了另外一种混杂系统:脉冲系统.它在离散时间内的状态会发生跳跃.最后,给出了一些数值例子来说明我们的结果.本文的主要工作包括以下部分:1.第二章研究了带有时滞的非线性随机切换系统的输入-状态稳定性问题.本文我们主要使用Lyapunov–Krasovskii方法,讨论了两种切换:1)同步切换;2)异步切换.对于同步切换,...
【文章页数】：125 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
Notation
Chapter 1 Introduction
1.1 Background
1.2 Main Research
1.2.1 ISS properties on switched stochastic systems
1.2.2 Research based on asynchronous switching
1.2.3 ISS properties for impulsive stochastic systems with delay impulse
1.2.4 Main contribution
Chapter 2 Lyapunov-Krasovskii function for switched stochastic systems
2.1 Model and problem formulation
2.2 Main results and their proofs
2.2.1 Stability analysis of the considered system under synchronous switching
2.2.2 Stability analysis of the considered systems under asynchronous switching
2.3 Numerical analysis
2.4 Conclusion
Chapter 3 Razumikhin theorem for switched stochastic systems
3.1 The model and the problem
3.2 Main results and their proofs
3.2.1 Razumikhin theorem for asynchronous switching
3.3 Numerical analysis
3.4 Conclusion
Chapter 4 The switching signals which prevail over the traditional ADT scheme
4.1 Model description and preliminaries
4.2 Stability analysis of switched stochastic nonlinear systems
4.3 Stability analysis of switched stochastic linear systems
4.4 Numerical analysis
4.5 Conclusion
Chapter 5 Impulsive stochastic systems with delayed impulses
5.1 Model description and preliminaries
5.2 Main results and their proofs
5.2.1 ISS property for impulsive stochastic nonlinear systems
5.2.2 Some subsystems are ISS for impulsive stochastic nonlinear systems
5.2.3 ISS property with multiple jump maps
5.3 Numerical analysis
5.4 Conclusion
Chapter 6 Conclusions and Prospects
6.1 Conclusions
6.2 Prospects
Bibliography
Publications or Finished Papers
Acknowledgements
本文编号：3925173
【文章页数】：125 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
Notation
Chapter 1 Introduction
1.1 Background
1.2 Main Research
1.2.1 ISS properties on switched stochastic systems
1.2.2 Research based on asynchronous switching
1.2.3 ISS properties for impulsive stochastic systems with delay impulse
1.2.4 Main contribution
Chapter 2 Lyapunov-Krasovskii function for switched stochastic systems
2.1 Model and problem formulation
2.2 Main results and their proofs
2.2.1 Stability analysis of the considered system under synchronous switching
2.2.2 Stability analysis of the considered systems under asynchronous switching
2.3 Numerical analysis
2.4 Conclusion
Chapter 3 Razumikhin theorem for switched stochastic systems
3.1 The model and the problem
3.2 Main results and their proofs
3.2.1 Razumikhin theorem for asynchronous switching
3.3 Numerical analysis
3.4 Conclusion
Chapter 4 The switching signals which prevail over the traditional ADT scheme
4.1 Model description and preliminaries
4.2 Stability analysis of switched stochastic nonlinear systems
4.3 Stability analysis of switched stochastic linear systems
4.4 Numerical analysis
4.5 Conclusion
Chapter 5 Impulsive stochastic systems with delayed impulses
5.1 Model description and preliminaries
5.2 Main results and their proofs
5.2.1 ISS property for impulsive stochastic nonlinear systems
5.2.2 Some subsystems are ISS for impulsive stochastic nonlinear systems
5.2.3 ISS property with multiple jump maps
5.3 Numerical analysis
5.4 Conclusion
Chapter 6 Conclusions and Prospects
6.1 Conclusions
6.2 Prospects
Bibliography
Publications or Finished Papers
Acknowledgements
本文编号：3925173
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