奇异摄动系统的鲁棒稳定性分析与反馈控制
发布时间:2017-12-31 08:03
本文关键词:奇异摄动系统的鲁棒稳定性分析与反馈控制 出处:《华东师范大学》2016年博士论文 论文类型:学位论文
更多相关文章: 奇摄动系统 鲁棒稳定 输入状态稳定 输出反馈 线性矩阵不等式 马尔克夫跳变系统 H_∞控制
【摘要】:两时标结构是奇异摄动系统或奇摄动系统固有的特性,这个特性通常会导致系统阶数的增加和刚性问题的产生.从而大大增加了对系统分析和控制的复杂性.为了克服上述问题的产生,奇摄动方法应运而生.在过去的40年,奇摄动方法获得了广泛的认可并在控制领域快速发展.目前,有关连续时间和离散时间两种情形下奇摄动系统理论的研究均己取得了很大的进展.本论文在深入研究奇摄动系统的鲁棒稳定以及反馈控制问题的基础之上,获得了一些新的结果,特别是离散奇摄动系统的研究,主要研究内容如下:(1)研究了连续和离散时间两种情形下具有非线性扰动的奇摄动系统的鲁棒稳定性与反馈控制问题.利用不动点定理和线性矩阵不等式技巧,给出了系统存在孤立根的充分条件.在此基础上,利用两时标方法分别获得了快慢子系统输入状态稳定的充分条件,利用给合方法的技巧,在系统内部稳定的条件下,进一步给出了全阶系统输入状态稳定的充分条件.同时,当系统内部不稳定时,给出了系统输入状态稳定反馈控制律的设计.(2)研究了离散时间奇摄动系统的H∞分析和控制问题.在时标分解的基础上,通过分析相应的快和慢子系统,首次给出了全阶系统具有给定的H∞性能指标的充分条件.同时,给出了闭环系统具有给定H∞性能指标的状态反馈控制律设计.(3)利用奇摄动方法,研究了离散时间奇摄动系统的严真动态输出的反馈控制问题.利用线性矩阵不等式技巧,分别对快和慢子系统的动态输出反馈控制器进行了设计,最后利用组合技巧,复合获得到原系统的动态输出反馈控制.结果显示,在复合动态输出反馈控制律作用下,当小参数充分小时,原系统是镇定的.(4)研究了离散时间奇摄动系统非严真的动态输出反馈控制问题.通过建立辅助系统的方法,将非严真的动态输出反馈控制问题转化为分别同时设计辅助系统的严真动态输出反馈与快子系统的静态输出反馈控制.结果显示,所提出的设计方法能保证原系统是镇定的.从而克服了对动态输出反馈控制严真要求的限制.(5)利用线性矩阵不等式技巧,研究了马尔克夫跳变奇摄动系统的H∞控制问题.给出了新的求解H∞控制器的方法.避免了求解非线性矩阵不等式和Riccati方程所带来的困难.并在此基出上给出了求解奇摄动系统的最大稳定界的方法.
[Abstract]:The structure of two timescale is the characteristic of singularly perturbed system or singularly perturbed system. This characteristic usually leads to the increase of system order and the generation of rigid problem, which greatly increases the complexity of system analysis and control. The singularly perturbed method came into being. In the past 40 years, the singularly perturbed method has been widely accepted and developed rapidly in the field of control. Great progress has been made on the theory of singularly perturbed systems in the case of continuous time and discrete time. In this paper, the robust stability and feedback control of singularly perturbed systems are studied in depth. Some new results are obtained, especially the study of discrete singularly perturbed systems. The main contents of the study are as follows:. The problem of robust stability and feedback control for singularly perturbed systems with nonlinear perturbations under both continuous and discrete-time conditions is studied. The fixed point theorem and the technique of linear matrix inequality are used. The sufficient conditions for the existence of isolated roots of the system are given. Based on this, the sufficient conditions for the stability of the input state of the fast and slow subsystems are obtained by using the two-time scale method, and the technique of the given combination method is used. Under the condition of internal stability of the system, the sufficient conditions for the stability of the input state of the full-order system are further given. At the same time, when the system is not stable inside the system. The H 鈭,
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