周期黎卡提微分方程正定解的存在性(英文)

陈阳舟; 陈善本

引用本文:	陈阳舟,陈善本.周期黎卡提微分方程正定解的存在性(英文)[J].控制理论与应用,2001,18(3):341~345.[点击复制]
	CHEN Yang-zhou,CHEN Shan-ben.Existence of Positive Definite Solution to Periodic Riccati Differential Equation[J].Control Theory and Technology,2001,18(3):341~345.[点击复制]

周期黎卡提微分方程正定解的存在性(英文)

Existence of Positive Definite Solution to Periodic Riccati Differential Equation

摘要点击 1560 全文点击 1007 投稿时间：1999-06-07 修订日期：2000-08-08

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DOI编号 10.7641/j.issn.1000-8152.2001.3.005

2001,18(3):341-345

中文关键词周期黎卡提微分方程埃尔米特周期正定(HPPD)解状态空间基底变换能稳性和能检测性

英文关键词 periodic Riccati differential equation Hermitian periodic positive definite(HPPD) solution state space basis transform stabilizability and detectability

基金项目

作者	单位
陈阳舟	北京工业大学电子信息与控制工程学院, 北京 100022
陈善本	上海交通大学焊接研究所, 上海 200030

中文摘要

讨论了标准的周期黎卡提微分方程. 给出了其存在埃尔米特周期正定(HPPD)解的一个完整的充分必要条件. 准确地说, 在经过一个适当的状态空间基底变换后该条件通过能稳性和能检测性概念表述. 结果表明, 当HP PD解存在时, 它或者是唯一的, 或者有无限多个. 这一结果可以看作是Richardson和Kwong的结果对周期时变情况的扩展.

英文摘要

This paper deals with the standard periodic Riccati differential equation. A complete necessary and sufficient condition is presented for the existence of Hermitian periodic positive definite(HPPD) solution. Precisely, after a proper change of basis in the state space the condition can be expressed in terms of the notions of stabilizability and detectability. Moreover, it is shown that when an HPPD solution exists, it is either unique, or else there are uncountably many such solutions. The result of the paper can be considered as a valid extension of Richardson and Kwong's result to the periodic version.