抄録
Matrix Riccati equations having constant coefficient matrices are known to have periodic solutions under certain conditions. The necessary and sufficient conditions for existence of general periodic solutions (covering non-negative definite, non-positive definite and indefinite solutions) are derived in this paper. Also the specific condition for existence of non-negative (or non-positive) definite and periodic solutions is clarified. Such conditions as well as computational procedures in deriving periodic solutions are demonstrated in the example. Self-excited oscillations inherent to matrix Riccati equations have significant implications, not only from the analytic point of view on Kalman filter and regulator problems, but also from the viewpoint of numerical integration of such equations.
