Convergence analysis of generalized conjugate direction method to solve general coupled Sylvester discrete‐time periodic matrix equations

Abstract

SummaryThe discrete‐time periodic matrix equations have been extensively applied as a main tool of analysis and design for periodic systems. This study is intended to provide a generalization of conjugate direction method for solving the general coupled Sylvester discrete‐time periodic matrix equations urn:x-wiley:acs:media:acs2742:acs2742-math-0001 The convergence theorem guarantees that the generalized conjugate direction method can compute the solutions of the general coupled Sylvester discrete‐time periodic matrix equations after a finite number of iterations in the absence of round‐off errors. Finally, numerical results are given to exhibit the accuracy and efficiency of the generalized conjugate direction method. Copyright © 2016 John Wiley & Sons, Ltd.

Three types of biconjugate residual method for general periodic matrix equations over generalized bisymmetric periodic matrices

“…Numerical methods for finding the approximate solutions of periodic matrix equations are being developed using some different approaches (Chu et al, 2007; Hajarian, 2015a, 2017a; Hossain and Uddin, 2017; Lv and Zhang, 2016, 2017). Wu et al (2018) proposed a novel iterative algorithm with a tuning parameter for finding the solutions of the forward discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic systems.…”