We present new iterative methods based on refinement process for solving large sparse Sylvesterobserver equations applied in state estimation of a continuous-time system. These methods use projection methods to produce low-dimensional Sylvester-observer matrix equations that are solved by the direct methods. Moreover, the refinement process described in this paper has the capability of improvin...

We discuss solvers for Sylvester, Lyapunov, and Stein equations that are available in the SLICOT Library (Subroutine Library In COntrol Theory). These solvers offer improved efficiency, reliability, and functionality compared to corresponding solvers in other computer-aided control system design packages. The performance of the SLICOT solvers is compared with the corresponding MATLAB solvers. T...

This paper presents a version of the Bartels-Stewart algorithm for solving Sylvester and Lyapunov equations that utilizes Jordan-Schur form equation matrices. The is type Schur which contains additional information about Jordan structure corresponding matrix. can be used to solve more efficiently in some cases. A two-level implemented allows us find directly non-scalar blocks solution These hav...

The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX +XB = C where A = (aij) ∈ Rn×n , B = (bij) ∈ Rm×m are crisp Mmatrices, C = (cij) ∈ Rn×m is fuzzy matrix and X ∈ Rn×m is unknown,by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)×(mn) fuzzy system of linear equatio...