An iterative algorithm for coupled Riccati equations in continuous-time Markovian jump linear systems

In this paper, a novel implicit iterative algorithm with some tuning parameters is developed to solve the coupled algebraic Riccati matrix equation arising in the continuous-time Markovian jump linear systems. By introducing some tuning parameters in the proposed iterative algorithm, the current estimation for unknown variables is updated by using the information not only in the last step but also in the current iterative step and previous iterative steps. These tuning parameters can be appropriately chosen such that the proposed algorithm has faster convergence performance than some previous algorithms. It is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive semidefinite solution of the coupled Riccati matrix equation if the corresponding Markovian jump system is stabilisable. Finally, an example is provided to show the effectiveness of the developed algorithm.