Finite iterative algorithm for solving coupled Lyapunov equations appearing in discrete-time Markov jump linear systems [Brief Paper]

An iterative algorithm for solving coupled algebraic Lyapunov equations appearing in discrete-time linear systems with Markovian transitions is established. The algorithm is computationally efficient since it can obtain the solution within finite steps in absence of round-off errors. Another feature of the proposed algorithm is that it can be implemented by using original coeffiecient matrices. A numerical example is given to show the effectiveness of the proposed algorithm.