An improved weighted iterative algorithm for Riccati matrix equation in discrete-time Markov jump system

This paper has come up with a novel iterative method which can obtain the unique solutions of the discrete coupled Riccati matrix equations. Firstly, with introducing a weighted parameter between the latest estimated information and the past information, we propose an iterative algorithm to solve the discrete coupled Riccati matrix equations. Then, the weighted parameter can be replaced with a diagonal parameter matrix to accelerate the convergence rate of solving the matrix equations. It makes further shown that the matrix sequence in the proposed algorithm can converge to the unique solutions of the matrix equation. In the end, a numerical example is shown to illustrate the feasibility of the iterative algorithm.