New results in the Lyapunov-type algorithm for algebraic MCV Riccati equations

In this paper, we give a new proof for the convergence of the Lyapunov-type algorithm which can be used to compute the iterative solutions of the coupled algebraic Riccati equations appearing in the minimal cost variance control problem. This proof uses existence argument of a positive definite solution of a standard algebraic Riccati equation. Moreover, we will show that this algorithm is well defined and converges to a unique pair of stabilizing solutions of the coupled algebraic equations under study. A mean result of this work is that the existence of this stabilizing solution does not depend on the detectability assumption.