An SOR implicit iterative algorithm for coupled Lyapunov equations

A novel implicit iterative algorithm is presented via successive over relaxation (SOR) iterations in this paper for solving the coupled Lyapunov matrix equation related to continuous-time Markovian jump linear systems. This algorithm contains a relaxation parameter, which can be appropriately chosen to improve the convergence performance of the algorithm. It has been shown that the sequence generated by the proposed algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the considered equation. Moreover, some convergence results of the presented SOR implicit iterative algorithm with arbitrary initial conditions are established, and a method to choose the optimal relaxation parameter for this algorithm is given. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithm.