Matrix Sign Function Methods for Solving Projected Generalized Continuous-Time Sylvester Equations

In this technical note, we investigate the numerical solution of the projected generalized Sylvester equations via a matrix sign function method. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Unlike the classical matrix sign function iteration, we propose a modification of the matrix sign function method that converges quadratically for pencils of arbitrary index. Numerical experiments report the effectiveness of the modified method.