This paper is devoted to the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. A parameter free iterative method is proposed. This method is based upon a combination of an approximate power method and a generalized ADI method. Numerical experiments presented in this paper show the effectiveness of the proposed method.

In this paper we propose a low-rank alternating direction implicit (ADI) method to solve projected generalized continuous-time Sylvester equations with low-rank right-hand sides. Such equations arise in control theory including the computation of inner products and norms, and the model reduction based on balanced truncation for descriptor systems. The requirements of this method are moderate with respect to both computational cost and memory. Numerical experiments presented in this paper show the effectiveness of the proposed method.