The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations

In this paper, the structure-preserving doubling algorithm (SDA) is considered to solve a discrete coupled Riccati matrix equation (DCRME) arising in Markov Jump Systems. Firstly, we transform the DCRME into a standard symplectic form using methods developed for symmetric structures. With the symplectic form, the SDA is established to obtain a positive definite solution to the DCRME. It is demonstrated that the matrix sequences generated by the SDA converge quadratically. Finally, the numerical example is provided to illustrate the effectiveness and feasibility of the presented SDA.