@article{Schneider1973GlobalAO,
title={Global aspects of the matrix Riccati equation},
author={C. R. Schneider},
journal={Mathematical systems theory},
year={1973},
volume={7},
pages={281-286}
}

Matrix Riccati equations are interpreted as differential equations on Grassman manifolds. Necessary conditions for the Riccati equation to be a Morse-Smale system are given in the autonomous and periodic cases. Under this condition, the equation is structurally stable and has a unique asymptotically stable equilibrium point or periodic solution.