Research on the theories and efficient numerical methods of M-­matrix algebraic Riccati equations (MARE) has become a hot topic in recent years. In this paper, we study the existence of minimal nonnegative solution for MARE and give a new proof to the existence of minimal nonnegative solution for the MARE associated with a regular M-­matrix, which is much simpler than the original proof. In addition, we give a wider condition to guarantee the existence of minimal nonnegative solution for the MARE, which is an extension of the existing results.

Algebraic, Riccati equation, Regular M--matrix; , Minimal nonnegative solution