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In the present paper, we consider large-scale continuous-time differentialmatrix Riccati equations having low rank right-hand sides. These equations aregenerally solved by Backward Differentiation Formula (BDF) or Rosenbrockmethods leading to a large scale algebraic Riccati equation which has to besolved for each timestep. We propose a new approach, based on the reduction ofthe problem dimension prior to integration. We project the initial problem ontoan extended block Krylov subspace and obtain a low-dimentional differentialalgebraic Riccati equation. The latter matrix differential problem is thensolved by Backward Differentiation Formula (BDF) method and the obtainedsolution is used to reconstruct an approximate solution of the originalproblem. We give some theoretical results and a simple expression of theresidual allowing the implementation of a stop test in order to limit thedimension of the projection space. Some numerical experiments will be given.

Low rank approximate solutions to large-scale differential matrix Riccati equations