Iterative algorithms with the latest update for Riccati matrix equations in Itô Markov jump systems

This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in Itô Markov jump systems. A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter. The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations. The convergence rate of the algorithm is dependent on the adjustable parameter. Furthermore, a numerical example is provided to show the effectiveness of the presented algorithms.