两类分布参数系统的稳定性

发布时间：2018-06-18 02:55

本文选题：分布参数系统 + 指数稳定性　；参考：《渤海大学》2016年硕士论文

【摘要】：控制方式、受控对象或控制器需要用分布参数描述的控制系统称为分布参数控制系统。在工程技术中除受控对象外,控制装置或执行机构也可能是分布参数系统。分布参数系统的稳定性是分布参数控制理论研究的主要内容之一,近些年来,受到广泛研究。在这样一种背景下,本文研究了具有观测时滞的单管热交换系统的指数稳定性和排队论系统的拟紧性与不可约性。对于具有观测时滞的单管热交换系统,首先利用算子半群理论,将闭环系统转化为Banach空间中的抽象Cauchy问题,通过验证系统算子生成一致有界半群,得到了系统存在唯一的时间依赖解;然后通过对系统算子谱分布与算子谱分布进行分析,得到系统半群的最终可微性与最终紧性,由此说明谱决定增长假设成立;最后,给出了一个与系统参数有关而合时滞无关的闭环系统的指数稳定性的充分条件。由于半群的拟紧性和不可约性与系统的指数稳定性有密切关系,因而利用抽象泛函分析方法研究了两个排队论系统的拟紧性与不可约性。更准确的说,由于系统适合Greiner的框架,因而应用Greiner的关于生成元边界扰动思想来研究上述问题。通过分析系统边界扰动算子的特殊性质得到系统算子生成半群的拟紧性和不可约性。利用这两个性质,讨论了两个排队论模型的指数稳定性。
[Abstract]:In control mode, the distributed parameter control system is called distributed parameter control system when the controlled object or controller needs to be described by distributed parameters. In engineering technology, in addition to controlled objects, control devices or actuators may also be distributed parameter systems. The stability of distributed parameter systems is one of the main contents of distributed parameter control theory, and has been widely studied in recent years. In this paper, the exponential stability and the quasi compactness and irreducibility of a single tube heat exchange system with observation delay are studied under such a background. For a single tube heat exchange system with observation delay, the closed loop system is transformed into an abstract Cauchy problem in Banach space by means of operator semigroup theory, and the uniformly bounded semigroup is generated by verifying the operator of the system. The existence and unique time-dependent solution of the system is obtained. By analyzing the spectral distribution of the operators and the spectral distribution of the operators, the final differentiability and the ultimate compactness of the semigroup of the system are obtained, which shows that the spectrum determines the hypothesis of growth. A sufficient condition for exponential stability of closed loop systems with time-delay independent of system parameters is given. Since the quasi-compactness and irreducibility of Semigroups are closely related to the exponential stability of systems, the quasi-compactness and irreducibility of two queueing systems are studied by using abstract functional analysis method. More accurately, because the system is suitable for Greiner's framework, we apply Greiner's idea of generating boundary perturbation to study the above problems. By analyzing the special properties of boundary perturbation operators, the quasi-compactness and irreducibility of semigroups generated by system operators are obtained. By using these two properties, the exponential stability of two queuing theory models is discussed.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O231

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