Finding solutions for periodic discrete-time generalized coupled Sylvester matrix equations via the generalized BCR method

The periodic discrete-time matrix equations have wide applications in stability theory, control theory and perturbation analysis. In this work, the biconjugate residual algorithm is generalized to construct a matrix iterative method to solve the periodic discrete-time generalized coupled Sylvester matrix equations The constructed method is shown to be convergent in a finite number of iterations in the absence of round-off errors. By comparing with other similar methods in practical computation, we give numerical results to demonstrate the accuracy and the numerical superiority of the constructed method.