Weighted Explicit Iterative Algorithms for Continuous Coupled Lyapunov Matrix Equations

This paper is concerned with the methods for solving continuous coupled Lyapunov matrix equations. First, based on the existing algorithms with latest estimation, a weighted explicit iterative algorithms is developed for solving the considered matrix equations. Second, it is shown that under zero initial conditions the sequence generated by the constructed algorithm monotonically converge to the unique positive definite solutions of the coupled Lyapunov matrix equations. In addition, some convergence results are presented for the algorithms with any initial conditions. Finally, a numerical example is provided to illustrate the effectiveness of the presented algorithms.