【作者】 杨丽；

【导师】 张庆灵；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2006， 博士

【摘要】 广义系统是一类形式更一般化的系统，是有着广泛的应用背景的动力系统，许多实际系统用广义系统模型描述起来更方便、自然，如交联大系统、经济系统、电子网络、电力系统和化工工程等。近年来，广义系统的理论与应用问题已经吸引了国内外众多学者的关注，并且已经取得了长足的进展。 耗散性系统理论自20世纪70年代提出以来，在系统稳定性研究过程中起到重要的作用，它的实质内容是存在一个非负的能量函数，使得系统能量损耗总是小于能量的供给率。耗散理论提出了一种控制系统设计与分析的思想，即从能量的角度，以输入输出的方式描述。耗散理论可以把一些数学工具与物理现象联系起来，使用于许多控制问题。在机电系统、机器人等控制应用方面和自适应控制、非线性H_∞控制等控制方面，已经证实了耗散控制是一种有效的方法。 本文对广义系统的耗散控制等问题进行了研究。全文的结构概括如下： (一)介绍了本文研究工作的背景。首先概述了广义系统的发展状况，并列举了一些实例，说明广义系统具有广泛的应用背景；其次分别介绍了耗散控制、无源控制的研究意义和发展现状；最后简要介绍了本文的主要工作。 (二)研究了广义系统、广义时滞系统的耗散控制和状态严格无源控制的问题。对于广义系统分别设计了耗散的、严格无源的状态反馈控制器；对于时滞广义系统，分别设计了耗散的、严格无源的无记忆状态反馈控制器和时滞状态反馈控制器，使得闭环系统是耗散的和状态严格无源的。 (三)在研究不确定广义系统耗散控制的同时消去了广义系统的脉冲行为。在状态空间下，通过解线性矩阵不等式得到了不确定广义系统对于允许的不确定性的脉冲耗散的状态反馈控制器和输出反馈控制器，这种控制器不仅使得闭环系统是无脉冲的，而且是耗散的。同样得到了脉冲无源的状态反馈控制器和输出反馈控制器，使得闭环系统是无脉冲而且是无源的。 (四)研究了一类非线性时滞系统的时滞相关的鲁棒耗散控制，利用解线性矩阵不等式得到了此类系统的时滞相关的鲁棒耗散的无记忆状态反馈控制器和时滞状态反馈控制器。同时，将时滞相关的耗散控制推广到广义系统中，研究了时滞广义系统的时滞相关的鲁棒耗散和鲁棒无源控制，同样也给出了时滞相关的鲁更多还原

【Abstract】 It is well known that the singular system has higher capability to describe physical system, and it is a kind of dynamical systems of more general and has widely applied background. Singular system models are more convenient and natural than normal models such as interconnected large-scale systems, economic systems, electrical network, power systems, chemical processes and so on. This is the reason why singular systems have attracted much interest in recent years, and they have been developed sufficiently.Dissipative theory plays an important role in the stability research of control systems since it was brought forward in 1970s, the implication is that there exists a nonnegative energy function (namely storage function) such that the energy consumption of a control system is always less than the supply rate of the energy. A kind of design and analytic idea is put forward in the dissipative theory, i.e. from the point of view of energy, and energy is described by input and output. Dissipative theory can contact some mathematic tools with physical phenomenon, and has been applied to many control problems. Dissipative theory has been approved to be a kind of effective method in machine system, robot control and adaptive control, nonlinear H_∞ control and so on.This thesis focuses on the problems of dissipative control for singular systems and is organized as follows:(1) The main background of the problem discussed in this thesis is introduced. Firstly, a brief introduction to singular systems is given, and some examples of singular systems are presented to illustrate the wide application in various fields; Secondly, the problems of dissipative control and passive control are introduced. Finally, the main work is summarized.更多还原