A Newton iterative method for coupled Lyapunov matrix equations

This article discusses the solution of continuous coupled Lyapunov equations via iterative techniques. By the principle of the Newton iterative approach, an iterative method is constructed for finding the solution of the considered equations. To improve convergence performance, two modified versions of the designed iterative methods are proposed by introducing a tuning parameter. For two modified Newton iterative methods, some convergence criteria are provided through the eigenvalue analysis of the corresponding iterative matrices. Specifically, a simple parameter selection method is provided for the implementation of the proposed modified iterative methods. Lastly, simulation examples are supported to exhibit the superiority of the developed Newton iterative methods than some existing methods.