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

Abstract

AbstractThere 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 AiXiBi+CiXi+1Di=Ei,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.