Convergence Characterization of an Iterative Algorithm for Continuous Coupled Lyapunov Matrix Equations

In this paper, the convergence characterization of a special implicit iterative algorithm with a tuning parameter for continuous coupled Markov jump Lyapunov matrix equation is investigated. First, a necessary condition for the convergence of the iterative algorithm is given. Then, a necessary and sufficient condition is proposed and the optimal tuning parameter such that the algorithm has the fastest convergence rate is analyzed in two cases according to the distribution of eigenvalues. Finally, a numerical example is given to illustrate the effectiveness of the algorithm and the effects of different tuning parameters.