Journal
IET CONTROL THEORY AND APPLICATIONS
Volume 7, Issue 14, Pages 1828-1833Publisher
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-cta.2013.0101
Keywords
conjugate gradient methods; Lyapunov matrix equations; polynomials; vectors; second-order Sylvester matrix equations; computational tools; Lyapunov matrix equations; Bi-CGSTAB method; vectorisation operator; Kronecker product; nonHermitian linear systems; coupled Sylvester matrix equations; bi-conjugate gradient stabilised method; matrix form
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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.
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