in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to ac...

We investigate the factorized solution of generalized stable Sylvester equations such as those arising in model reduction, image restoration, and observer design. Our algorithms, based on matrix sign function, take advantage current trend to integrate high performance graphics accelerators (also known GPUs) computer systems. As a result, our realisations provide valuable tool solve large-scale ...

Based on the well-known Leverrier algorithm, a simple explicit solution to right factofization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback a...

Sylvester equations play a central role in many areas of applied mathematics and in particular in systems and control theory. Here we will show how low-rank solutions for stable Sylvester equations can be computed based on the matrix sign function method. We discuss applications in model reduction as well as in observer design. Numerical experiments demonstrate the efficiency of the proposed me...