Existence of Positive Definite Solution to Periodic Riccati Differential Equation
周期黎卡提微分方程正定解的存在性

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.