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

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.