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关于控制系统稳定性、可控可观性若干问题的研究
Alternative TitleA Study of Several Problems about Stability、Controllability and Observability of Control Systems
王成红
Subtype工学博士
Thesis Advisor疏松桂
1997-07-01
Degree Grantor中国科学院自动化研究所
Place of Conferral中国科学院自动化研究所
Degree Discipline控制理论与控制工程
Keyword稳定性 可控性与可观测性 线性系统 线性区闻系统 非线性定常系统 连续非线性系统 游荡不存在条件 吸引域估计 Stability Controllability And Observability Linear Interval Systems Nonlinear Autonomous Systems Continuous Nonlinear Systems Wa
Abstract稳定性、可控性与可观测性是控制系统三大主要属性,其相应的理论是控制理论的基 础。本文研究了控制理论中与这三个属性有关的几个问题,它们分别是:(1)多变量线性定 常连续系统可控可观与其相应的离散系统可控可观之间的关系;(2)线性区间系统的稳定 性;(3)线性区间系统的可控可观测性;(4)非线性定常系统全局渐近稳定性;(5)连续非线 性系统在给定域内(上)游荡不存在条件;(6)连续非线性系统平衡点吸引域的估计。本文关 于上述六个问题的具体研究内容和所取得的成果如下: (1)揭示了线性系统理论中几个有用的关系;给出了线性定常连续系统状态完全可控、 可观、或既可控又可观,其相应的离散系统也状态完全可控、可观、或既可控又可观的充分必 要条件。 (2)用区间分析的方法研究了线性区问系统的稳定性。给出了区间Routh判据及用区 间Routh判据分析区间多项式Hurwitz性的方法;给出了区间多项式Schur性的分析方法; 给出了区问矩阵行列式的定义及计算公式;给出了特征区问矩阵、特征区问多项式的定义及 将特征区间多项式化为一般区间多项式的方法;给出了用区间Routh判据判定线性区间系 统为稳定的必要条件和充分条件。 (3)用区间矩阵秩和区间矩阵行列式理论研究了线性区问系统的可控性与可观测性, 得到了线性区问系统可控、可观的必要条件.及一些特殊线性区间系统可控、可观的充分必 要条件。给出了线性区间系统的可控、可观和既可控又可观标准形。 (4)给出了Krasovskii全局渐近稳定性定理的一个等价定理.在此基础上,给出了非线 性定常系统全局渐近稳定的几个新结果。 (5)给出了连续非线性系统在给定域内(上)游荡的定义,及游荡不存在条件。这些游荡 不存在条件不仅可以判断闭轨、极限环、极限环面的不存在,而且可以判断一切具有振荡共 性的系统轨迹在给定域内(上)不存在。 (6)研究了连续非线性系统平衡点吸引域的估计问题;揭示了渐近稳定平衡点之吸引 域及吸引域边界与不稳定平衡点之间的关系;揭示了渐近稳定平衡点之吸引域与系统对称 性之间的关系。给出了单调吸引域的定义,单调吸引域与吸引域之间的关系,及利用单调吸 引域估计吸引域的方法。
Other AbstractStability, Controllability and Observability are three principal properties of control systems,and the theory about them is main basis of control theory. Several problems in control theory relative to stability,Controllability and Observability are studied in the dissertation,and they are respectively : (1) relationships between controllability with observability of a multivariable linear time-invariant system and controllability with observability of its corresponding discrete system; (2) stability of linear interval systems; (3) controllability and observability of linear interval systems; (4) global asymptotic stability of nonlinear autonomous systems; (5) conditions that continuous nonlinear systems don't wander in (on) a given domain; and (6) estimation of attraction domains of equilibrium points of a continuous nonlinear system. Concrete research contents and results which have been gotten on six problems mentioned above are as follows : (1) Revealing several useful relationships in linear system theory ,and presenting sufficient and necessary conditions that all states of a linear time--invariant system are controllable,observable, or both controllable and observable, and all states of its corresponding discrete system are also controllable, observable ,or both controllable and observable. (2) Studying stability of linear interval systems by the method of interval analysis. Giving Routh criterion of interval and methods analyzed Hurwitz property of an interval polynomial by using of Routh criterion of interval. Giving analytic methods for Schur property of a discrete interval polynomial. Presenting the determinant definition and the computational formula of an interval matrix. Presenting definitions of a characteristic interval matrix and a characteristic interval polynomial, and methods translated a characteristic interval polynomial into an interval polynomial. And presenting necessary conditions and sufficient conditions judging a linear interval system to be stable by using of Routh criterion of interval. (3) Studying controllability and observability of a linear interval system by means of the theory of an interval matrix's rank and its determinant, and getting necessary conditions that a linear interval system is controllable, or observable, and sufficient and necessary conditions where linear interval systems are special ones. Giving controllable standard forms, observable standard forms, and both controllable and observable standard forms of linear interval systems. (4) Presenting one global asymptotic stability theorem which equals to Krasovskii's ones, and on the basis of that, presenting several new results on global asymptotic stability of nonlinear autonomous systems. (5) Presenting definitions of wanderings and conditions that wanderings are inexistent of a continuous nonlinear system in (on) a given domain. By these conditions, not only a system's closed loci,limit cyc
shelfnumXWLW411
Other Identifier411
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/5675
Collection毕业生_博士学位论文
Recommended Citation
GB/T 7714
王成红. 关于控制系统稳定性、可控可观性若干问题的研究[D]. 中国科学院自动化研究所. 中国科学院自动化研究所,1997.
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