AJGI iterative algorithm for solving coupled Sylvester matrix equations with one side

This paper considers the coupled Sylvester matrix equations with one side, which have many important applications in control theory and system theory. Based on the Jacobi iterative method and the hierarchical identification principle, the Jacobi-gradient based iterative algorithm and the accelerated Jacobi-gradient based iterative algorithm are constructed. It is theoretically proved that the presented algorithms are convergent for any initial matrix under appropriate conditions, and numerical examples are given to show that the presented iterative algorithms are faster than some existing iterative algorithms. Moreover, the application of the accelerated Jacobi-gradient based iterative algorithm in dynamical systems is presented.