Periodic oscillations of matrix Riccatti equations in time-invariant systems

Periodic oscillations arising in matrix Riccati equntions having constant coefficient matrices are investigated in this paper. The algorithm deriving such periodic solutions and the condition for their existence are obtained. Since matrix Riccati equations play a crucial role in optimal estimation and control theories, tn scattering theory, and in other important applications, the stability of solutions has grave implication. Such analysis is also vital from the viewpoint of numerical integrations of Riccati equations.