CASIA OpenIR  > 毕业生  > 博士学位论文
线性正系统中最小正实现问题的研究
其他题名Research on Minimal Positive Realizations of Linear Positive Systems
孙燏伟
学位类型工学博士
导师郁文生
2008-05-31
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学位专业控制理论与控制工程
关键词线性正系统 最小正实现 正分解 非负矩阵 分格系统 位相型分布 Positive Linear Systems Minimal Positive Realizations Positive Decomposition Problem Nonnegative Matrix Compartmental Systems Phase-type Distributions
摘要正系统理论广泛应用于光纤滤波、化学工程、生物医药、经济学、社会学等多种领域,而最初源于隐马尔科夫模型辨识的正实现问题是正系统理论中的一个基本问题,受到研究人员的大量关注。 本文主要讨论了单输入单输出线性时不变离散时间系统和连续时间系统的最小正实现问题。针对离散时间系统,采用构造性的方法,给出系统存在等阶正实现的条件,并将得到的结论用于解决正分解问题,降低了实现的阶数。针对连续时间系统,采用平移变换的方法,将离散时间系统的结果推广到连续时间系统,得到连续时间系统存在等阶正实现的条件,得到的结论可以用于分格系统的辨识和确定位相型分布的表示。每种情况都有数值例子表明结果的有效性。 本文中主要的工作和贡献有: 1、讨论了三阶具有复极点的离散时间系统和连续时间系统存在三阶正实现的条件。针对离散时间系统,根据复极点的分布,将传递函数分为两类。针对其中一类传递函数,给出了其存在三阶正实现的充分必要条件,针对另一类,给出其存在三阶正实现的充分性条件。采用平移变换的方法,得到了连续系统存在三阶正实现的充分性条件。得到的结论推广了文献中已有的结论。 2、针对n阶离散时间单输入单输出线性时不变有理传递函数H(z)具有(n-1)个负极点的情况,采用构造性的方法,得出了其存在等阶正实现的充分必要条件;当n阶离散时间单输入单输出线性时不变有理传递函数H(z)具有复极点时,给出了此类传递函数存在等阶正实现的充分性条件,并且当传递函数的极点之和为零时,得到的条件具有必要性。 3、针对n阶连续时间单输入单输出线性时不变有理传递函数H(s)分别具有互异的和重复的实数极点的情况,分类讨论了传递函数存在n阶正实现的条件;当连续时间单输入单输出线性时不变有理传递函数H(s)具有复数极点时,借助正性指数的概念,给出了此类传递函数存在具有一定正性指数的等阶正实现的充要条件。 4、将本文得到的最小正实现结论应用于正分解问题的讨论,改进了已有的结论,降低了正分解问题中实现的阶数,并且给出了一个算法,指出了进一步降低阶数的可能性。
其他摘要Positive systems theory can be widely applied in various fields, such as optical filtering, chemical engineering, biology and medicine, economics, social science etc, and positive realization problem, which arose from identification of hidden Markov model, is a basic problem of positive systems theory, and draws great attention from researchers. This dissertation focuses on minimal positive realizations of nth-order rational transfer functions of discrete-time and continuous-time linear time-invariant single-input-single-output (SISO) systems. For discrete-time systems, with the help of constructive methods, conditions are provided for nth-order systems to have nth-order positive realizations, which can be applied to reducing the order of realizations in positive decomposition problem. For continuous-time systems, with the method of transformation, the results are deduced from those of discrete-time systems, which can be applied to deciding the minimal compartment number of a compartmental system and to finding a representation for a phase-type (PH) distribution. In each case, numerical examples are employed to validating the effectiveness of the obtained results. The main contributions of this dissertation include following issues: 1. Conditions are provided for third order discrete-time and continuous-time systems with complex poles to have third order positive realizations. For discrete-time systems, according to the location of the complex poles, transfer functions are divided into two groups. For one group, necessary and sufficient conditions are provided for existence of third order positive realizations; for the other, sufficient conditions are provided. With the method of shifting transformation, sufficient conditions are obtained for continuous-time transfer functions to have third order positive realizations. These results improve the existing ones in literatures. 2. With constructive methods, necessary and sufficient conditions are obtained for nth order transfer functions H(z) with (n-1) negative poles to have nth-order positive realizations; and sufficient conditions are presented for a class of nth-order transfer functions H(z) with complex poles to have nth-order positive realizations. However, the obtained conditions are necessary, in case that the sum of poles is equal to zero. 3. For nth-order continuous-time transfer functions H(s) of distinct, or multiple real poles, conditions are provided for H(s) to have nth-order positive realizations, respectively. For nth-order transfer functions with complex poles, with the help of index of positivity, necessary and sufficient conditions are provided for H(s) to have nth-order positive realizations with certain index of positivity.
馆藏号XWLW1247
其他标识符200518014628033
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/6108
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
孙燏伟. 线性正系统中最小正实现问题的研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2008.
条目包含的文件
文件名称/大小 文献类型 版本类型 开放类型 使用许可
CASIA_20051801462803(706KB) 暂不开放CC BY-NC-SA请求全文
个性服务
推荐该条目
保存到收藏夹
查看访问统计
导出为Endnote文件
谷歌学术
谷歌学术中相似的文章
[孙燏伟]的文章
百度学术
百度学术中相似的文章
[孙燏伟]的文章
必应学术
必应学术中相似的文章
[孙燏伟]的文章
相关权益政策
暂无数据
收藏/分享
所有评论 (0)
暂无评论
 

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。