An implicit iterative algorithm for algebraic Riccati matrix equations

In this paper, an implicit iterative algorithm is proposed to obtain the unique positive definite solution of the continuous algebraic Riccati matrix equation. In this proposed algorithm, there exists a tuning parameter which can be appropriately chosen such that the algorithm achieves better convergence performance. A sufficient condition is given for the convergence of the proposed algorithm. Moreover, an approach is also provided to choose an appropriate initial condition. Finally, a numerical example is employed to show the effectiveness of the proposed algorithm.