Matrix form of the Bi-CGSTAB method for solving the coupled Sylvester matrix equations

The bi-conjugate gradient stabilised (Bi-CGSTAB) method is one of the efficient computational tools to solve the non-Hermitian linear systems Ax=b. By employing Kronecker product and vectorisation operator, this study investigates the matrix form of the Bi-CGSTAB method for solving the coupled Sylvester matrix equations Sigma(k)(i=1) (A(i)XB(i) + CiYDi) = M, Sigma(k)(i=1)(EiXFi + G(i)YH(i)) = N [including (second-order) Sylvester and Lyapunov matrix equations as special cases] encountered in many systems and control applications. Several numerical examples are given to compare the efficiency and performance of the investigated method with some existing algorithms.