In this paper, a novel implicit iterative algorithm with some tuning parameters is developed to solve the coupled algebraic Riccati matrix equation arising in the continuous-time Markovian jump linear systems. By introducing some tuning parameters in the proposed iterative algorithm, the current estimation for unknown variables is updated by using the information not only in the last step but also in the current iterative step and previous iterative steps. These tuning parameters can be appropriately chosen such that the proposed algorithm has faster convergence performance than some previous algorithms. It is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive semidefinite solution of the coupled Riccati matrix equation if the corresponding Markovian jump system is stabilisable. Finally, an example is provided to show the effectiveness of the developed algorithm.

中文翻译：

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连续时间马尔可夫跳跃线性系统中耦合Riccati方程的迭代算法

在本文中，开发了一种具有一些调谐参数的新型隐式迭代算法来求解连续时间马尔可夫跳跃线性系统中出现的耦合代数Riccati矩阵方程。通过在所提出的迭代算法中引入一些调整参数，不仅在最后一步而且在当前迭代步骤和先前迭代步骤中使用信息更新对未知变量的当前估计。可以适当地选择这些调整参数，使得所提出的算法比一些以前的算法具有更快的收敛性能。结果表明，如果相应的马尔可夫跳跃系统是稳定的，则该算法在零初始条件下可以单调收敛到耦合Riccati矩阵方程的唯一正半定解。最后，