An Iterative Algorithm with a Tuning Parameter for Continuous Lyapunov Matrix Equations

In this paper, by introducing a tuning parameter, an explicit iterative algorithm is constructed for solving the continuous Lyapunov matrix equations associated with Itô stochastic systems. A necessary and sufficient condition is provided to guarantee the convergence of the proposed algorithm by using the Kronecker product. Moreover, some easily verifiable convergence results are developed for the proposed algorithm based on the obtained necessary and sufficient condition. In addition, a method is given for the selection of the optimal tuning parameter. Finally, an example is applied to verify the effectiveness of the presented algorithm.