This letter is concerned with the decentralized $H_{\infty }$ control problem of discrete-time interconnected systems. The studied interconnected system is transformed equivalently into a single linear time invariant system with matrix inversion terms in the system matrices. This letter derives novel necessary and sufficient conditions such that the considered interconnected system is asymptotically stable with the prescribed $H_{\infty }$ performance. The new conditions are computationally attractive because of the elimination of matrix inversion terms. Then these conditions are transformed into linear matrix inequalities. The decentralized controllers can be obtained by solving linear matrix inequalities to guarantee the stability and the $H_{\infty }$ performance of the closed-loop interconnected system. Finally, the effectiveness and the advantages of the proposed results are demonstrated by one numerical example.

中文翻译：

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离散关联系统分散H∞控制的新充要条件。

这封信与权力下放有关 $ H _ {\ infty} $ 离散时间互连系统的控制问题。所研究的互连系统等效地转换为一个单线性时不变系统，该系统在系统矩阵中具有矩阵求逆项。这封信得出新颖的必要条件和充分条件，以使所考虑的互连系统在规定的条件下渐近稳定 $ H _ {\ infty} $ 表现。由于消除了矩阵求逆项，因此新条件在计算上具有吸引力。然后将这些条件转换为线性矩阵不等式。可以通过求解线性矩阵不等式来获得分散控制器，以保证稳定性和稳定性。 $ H _ {\ infty} $ 闭环互连系统的性能。最后，通过一个数值例子证明了所提出结果的有效性和优势。