In this paper, base on the theory of the non‐symmetric algebraic Riccati equation and the coupled Riccati equation, we give the general form of the non‐symmetric coupled algebraic Riccati equation (NCARE). In order to effectively solve the minimal non‐negative solution of the NCARE, two numerical iteration methods are improved: inexact Newton method (INewton) and alternate linear implicit method (ALI). Further, we give the convergence theory of the two iteration methods. Finally, we offer numerical examples to show the effectiveness of the derived methods.

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