A direct method for solving projected generalized continuous-time Sylvester equations

Abstract This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula...
Ausführliche Beschreibung

Abstract This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula of the solution of the projected generalized continuous-time Sylvester equation is presented. A direct method based on the generalized Schur factorization is proposed. Moreover, its low-rank version for problems with low-rank right-hand sides is also proposed. The computational cost of the direct method is estimated. Numerical simulation show that this direct method has high accuracy. Ausführliche Beschreibung