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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 .
We discuss the standard periodic Riccati differential equation and give a complete necessary and sufficient condition for the existence of Hermite periodic positive definite (HPPD) solutions. To be exact, after a proper state-space transformation, It is expressed by the concept of stability and detectability.The results show that when the HPPD solution exists, it is either unique or infinitely many.The results can be seen as the result of Richardson and Kwong’s analysis of the time-varying periodicity The expansion.