Iterative algorithms for solving continuous stochastic Lyapunov equations

In this study, a novel iterative algorithm is proposed for solving coupled Lyapunov equations appearing in continuoustime Itô stochastic systems with Markovian jump parameters. In this algorithm, some tunable parameters are introduced, and thus a combination of the information in both the last step and the current step can be utilised to update the estimation of the unknown matrix variables. The monotonicity and boundedness of the proposed algorithm are analysed, and the convergence condition for this algorithm is also given. Due to the use of the latest updated information, the proposed algorithm can achieve better convergence performance than the existing iterative algorithm by appropriately choosing the tuning parameters. An illustrative example is employed to show the effectiveness of the proposed algorithm.