【作者】 陈霞；

【导师】 李春吉；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2012， 硕士

【摘要】 随着科学技术的发展,切换系统作为一种重要的混杂系统越来越受到国内外控制界的关注。在实际的工程系统中,由于系统的某些的特性及人们对系统缺乏了解,导致不确定性和时滞现象普遍存在,进而破坏的系统的稳定性。近年来,关于不确定时滞切换系统的研究已经有一些成果,但是对不确定多时滞切换系统的H∞控制及对不确定时滞切换系统的非脆弱H∞状态反馈控制器的设计的研究还是比较少的。不确定性、多时滞现象及脆弱性是在系统中经常出现的,因此,针对这两个问题研究具有十分重要的意义。本文以现有的切换系统的研究成果作为基础,结合H∞控制理论,基于Lyapunov稳定性理论及线性矩阵不等式等,对不确定多时滞切换系统的H∞控制,及不确定时滞切换系统在特定切换信号及任意切换信号下的非脆弱状态反馈H∞控制进行了研究。主要内容如下：首先,介绍了切换系统的研究背景及研究现状,阐述了H∞控制理论的发展状况,说明了对不确定时滞切换系统H∞控制问题研究的重大意义；然后又介绍了切换系统的一些基本概念,Lyapunov稳定性理论和线性矩阵不等式的一些基本内容,以及用到的一些引理。其次,对不确定多时滞切换系统的H∞控制问题进行了研究。给出了不确定多时滞切换系统满足H∞干扰抑制水平γ可切换镇定的充分条件,并且在非自治系统中,给出了存在H∞状态反馈控制器的充分条件,在最后用数值算例验证了所得结果的有效性。再次,介绍了不确定时滞切换系统的非脆弱状态反馈H∞控制问题。在不确定时滞切换系统中针对解决鲁棒问题时遇到的脆弱性,分别在特定切换信号和任意切换信号下,给出了存在非脆弱H∞状态反馈控制器的充分条件,并且分别给出了数值算例,验证了其有效性。最后,总结了全文并对不确定时滞切换系统的研究提出了展望。更多还原

【Abstract】 With the development of science and technology, the switched systems as important hybrid systems have received more and more concerns from domestic and foreign control sector. In practical engineering systems, some of the characteristics of the system and lack of understanding of the system lead to uncertainty and time-delay widespread, and thus undermine the stability of the systems. In recent years, some researches on the uncertain time-delay switched systems have success, but the research on the uncertain multiple-delays switched systems and the design of non-fragile state feedback control of uncertain time-delay switched systems is rare. Uncertain multi-time delay phenomenon and the fragile often appear, so it has great significance to study the two problems.Based on current research achievements of switched systems, stability theory of Lyapunov function and linear matrix inequalities, combined with control theory, we consider H∞control for uncertain multi-time delay switched systems and non-fragile state feedback H∞control of uncertain switched systems with time-delay in the particular switch signal and arbitrary signals. The main content are as follows:Firstly, we introduce the research background and status of switched systems, expound the developing situation of the control theory, show the great significance of researching H∞control of the uncertain time-delay switched systems. And in the paper, we introduce some basic concepts, the stability theory of Lyapunov function and some basic contents of linear matrix inequality, as well as some lemmas used in researching.Secondly, we discuss the H∞control of uncertain multi-time delay switched systems, give the sufficient conditions of H∞control of the uncertain multi-time delay switched systems. And we give the sufficient conditions of exciting H∞state feedback controller in non-autonomous systems. Thus a numerical example is given to show the feasibility of the results.Thirdly, we study the non-fragile state feedback H∞control problem of uncertain time-delay switched systems. In the uncertain time-delay switched systems, according to the fragile in solving the robust problem, we give respectively the sufficient conditions of exciting non-fragile state feedback H∞controller in particular switching signal and arbitrary switching signal. And then the numerical example is given to verify its validity.Finally, concluding remarks are presented, and some problems which deserve further study of the uncertain time-delay switched systems are also pointed out.更多还原