New Iterative Algorithms for Solving Coupled Markovian Jump Lyapunov Equations

In this technical note, two iterative algorithms are developed for solving the coupled Lyapunov matrix equations associated with discrete-time Markovian jump linear systems. Some convergence results have been obtained for these algorithms. The new algorithms are different from the previous results in nature and they can be regarded as sequential versions of the parallel algorithm reported in the work of Borno and Gajic. Numerical experiments show that the proposed algorithms are faster in terms of the number of iterations to achieve the desired accuracy.