In this paper, we discuss the existence of the positive solution for the coupled algebraic Riccati equation which is usually encountered in control theory. When this equation has a positive solution, Newton’s method is presented to find the minimal positive solution. Furthermore, we show some properties of Newton’s iteration method. Finally, we give corresponding numerical examples to demonstrate the effectiveness of the derived iteration method.

中文翻译：

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牛顿法求解耦合代数Riccati方程的正解并应用于自动控制

在本文中，我们讨论了控制理论中经常遇到的耦合代数Riccati方程正解的存在性。当该方程具有正解时，提出了牛顿法来寻找最小正解。此外，我们展示了牛顿迭代方法的一些特性。最后，我们给出相应的数值示例，以证明派生迭代方法的有效性。