Finite iterative algorithm for solving Lyapunov equations of Itô stochastic systems with Markovian jumps

An iterative algorithm is given to find an exact solution to the coupled Lyapunov matrix equations of the discrete-time Itô stochastic liner systems with Markovian jumps. It has been proved that the algorithm can obtain the solution within finite steps in absence of round-off errors, and has fast convergence speed and good numerical stability. The algorithm is explicit iteration, which avoids the influence of the errors generated during the process of solving the other matrix equations.