Gradient-based iterative approach for solving constrained systems of linear matrix equations

Coupled linear matrix equations arise in many fields of engineering, including control theory, system identification, and signal processing. In this manuscript, we propose an iterative algorithm based on the generalized shift-splittings and using the hierarchical identification principle (GSSHIP) approach for efficiently solving coupled Sylvester matrix equations. The efficacy of the iterative methods presented in this study has been demonstrated through the use of some numerical examples. Finally, we will explore the practical implementation of the proposed approach utilizing Newton's method to solve continuous-time algebraic Riccati matrix equations.