  Matrix Riccati differential equations arise in many different areas and are
particular important within the field of control theory. In this paper we
consider numerical integration for large-scale systems of stiff matrix Riccati
differential equations. We show how to apply exponential Rosenbrock-type
integrators to get approximate solutions. Two typical exponential integration
schemes are considered. The implementation issues are addressed and some
low-rank approximations are exploited based on high quality numerical algebra
codes. Numerical comparisons demonstrate that the exponential integrators can
obtain high accuracy and efficiency for solving large-scale systems of stiff
matrix Riccati differential equations.
