%0 Journal Article
%T Existence of Positive Definite Solution to Periodic Riccati Differential Equation<br>周期黎卡提微分方程正定解的存在性
%A CHEN Yang-zhou
%A CHEN Shan-ben
%A <br>陈阳舟
%A 陈善本
%J 控制理论与应用
%D 2001
%I 
%X 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.
%K periodic Riccati differential equation
%K Hermitian periodic positive definite (HPPD) solution
%K state space basis transform
%K stabilizability and detectability<br>周期黎卡提微分方程
%K 正定解
%K 存在性
%K 状态空间基底变换
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=970898A57DFC021F93AB51667BAED7F7&aid=AC4A871627647B87&yid=14E7EF987E4155E6&vid=13553B2D12F347E8&iid=38B194292C032A66&sid=4B168891B5E5FB30&eid=3622B70F9C54A9CC&journal_id=1000-8152&journal_name=控制理论与应用&referenced_num=0&reference_num=13