【作者】 宋敏；

【导师】 李春吉；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 在一些实际领域,许多问题都是以广义系统来建模的,像捕食系统、电力系统、人口增长模型等。相对于状态空间系统广义系统能更好地描述物理系统。另一方面,时滞常常出现在各类系统中,如化学、生物、神经及其它自然系统。它通常是控制系统不稳定和性能下降的根源。同时,在各种物理、工业和工程系统中,由于模型简化、环境变化和元件老化等原因,不可避免地会出现各种不确定性,因此,对时滞广义系统,特别是不确定时滞广义系统的分析与综合具有十分重要的理论和实际意义。本文内容概况如下：第一章：介绍了广义系统的背景、理论发展和研究现状。第二章：介绍了广义系统的一些基础知识,以及后面研究工作用到的定义、定理及引理。第三章：针对多时滞广义系统研究了其容许性问题。通过构造新的Lyapunov泛函,首先给出了全新的多时滞广义系统的稳定性判据,之后,在此基础上得到了时滞相关状态反馈镇定控制器的设计方法。第四章：通过利用Lyapunov-krasovskii方法和增广模型变换方法,首次得到快变时滞广义系统的导数积分比例反馈镇定方法；针对含有范数有界的不确定性的有界快变时滞广义系统,得到其导数积分比例反馈鲁棒镇定方法。第五章：对全文的工作做了总结,同时也对进一步的研究工作进行了展望。更多还原

【Abstract】 In many practical fields, it has been found that many problems are modeled by singular systems, such as predator-prey interactions, power systems, population growth models and so on. Singular systems can better describe physical systems than regular ones. On the other hand, time-delay is often countered in various engineering systems, such as chemical, biological, neural and other natural systems, and it is an important source of instability and poor performance. Also, uncertainties inevitably exist in all kinds of physical, industrial and engineering systems because of the simplification of model, change of running environment, and aging of electrical elements and so on. Therefore, the analysis and synthesis for singular systems with time-delay, especially for uncertain singular systems with time-delay are important both in theory and practice.The main contents of this paper are as followed:(1) In chapter 1, the background, the development of the theory and resent research achievements of singular systems are introduced respectively.(2) In chapter 2, the fundamental knowledge of singular systems is introduced. Some definitions, theorems and lemmas which will be used later are presented.(3) In chapter 3, the problem of admissibility for singular systems with multiple time-varying delay is studied. By constructing a new Lyapunov function, first, we develop a delay-dependent sufficient condition, which guarantees that the system is admissible. Then, based on this, a delay-dependent sufficient condition for the existence of a state feedback controller which guarantees that the corresponding closed-loop system is admissible is presented.(4) In chapter 4, for singular systems with bounded fast time-varying state time-delay, by using Lyapunov-krasovskii method and augmented model, a delay-dependent criterion which guarantees that the corresponding closed-loop systems is normal and stable is presented. And for singular systems with bounded fast time-varying state delay and norm-bounded uncertainties, robust PID controller can also be designed.(5) In chapter 5, a conclusion is given. And the perspective on the furthermore study is also proposed.更多还原