4.4 Article

Matrix form of Biconjugate Residual Algorithm to Solve the Discrete-Time Periodic Sylvester Matrix Equations

Journal

ASIAN JOURNAL OF CONTROL
Volume 20, Issue 1, Pages 49-56

Publisher

WILEY
DOI: 10.1002/asjc.1528

Keywords

BCR algorithm; Sylvester discrete-time periodic matrix equation; Lyapunov discrete-time periodic matrix equation

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There are important relationships between the discrete-time linear periodic descriptor systems and the discrete-time periodic matrix equations. In the present paper, we introduce the matrix form of the biconjugate residual (BCR) algorithm for solving the discrete-time periodic Sylvester matrix equations A(i)X(i)B(i)+CiXi+1Di=E-i,i=1,2,.... It is shown that the introduced algorithm converges to the solutions within a finite number of iterations in the absence of round-off errors. Finally, three numerical examples are given to demonstrate the efficiency and the performance of the algorithm.

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