Explicit Iterative Algorithms for Continuous Coupled Lyapunov Matrix Equations

Two explicit iterative algorithms are developed in this paper for solving continuous coupled Lyapunov matrix equations. By introducing a tunable parameter, the considered matrix equations are transformed into the Kalman-Yakubovich matrix equations. Further, based on the obtained equations, an explicit iterative algorithm is constructed to solve the coupled Lyapunov matrix equations. In addition, by using the latest estimation an improved iterative algorithm is proposed. Some convergence results are obtained for the presented improved iterative algorithm. It is shown that the convergence performance of the proposed algorithms can be significantly improved if the tunable parameter can be properly chosen. Finally, a numerical example is given to show the merit of the presented algorithms.