A method to solve the discrete-time coupled algebraic Riccati equations

We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control. Two iterations for computing a symmetric solution of this system are investigated. New iterations are based on the properties of a Stein equation. It is necessary to solve a Stein equation at each step of proposed algorithms. We adapt the conditions for convergence several previous iterations presented in the literature for solving rational Riccati equations arising in stochastic control.