In this paper, we investigate discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). First, the well-posedness, quadratic stability and contractiveness of discrete-time USISs are introduced. Second, a sufficient condition is proposed to guarantee that discrete-time USISs are well-posed, quadratically stable and contractive. Then, a more tractable condition is derived to check the well-posedness, quadratic stability and contractiveness of discrete-time USISs via a modified bilinear transformation. Besides, the robust distributed filters which inherit the structure of the plants are designed. A sufficient and necessary condition is presented to guarantee the existence of the robust distributed filters. Finally, a vehicle platoon model demonstrates the effectiveness of the proposed scheme.

中文翻译：

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具有 LFT 不确定性的离散时间空间互连系统的鲁棒分布式滤波器设计

在本文中，我们研究了离散时间不确定性空间互连系统 (USIS)，其中不确定性通过线性分数变换 (LFT) 进行建模。首先，介绍了离散时间USIS的适定性、二次稳定性和收缩性。其次，提出了保证离散时间 USIS 适定、二次稳定和收缩的充分条件。然后，通过改进的双线性变换导出了一个更易于处理的条件来检查离散时间 USIS 的适定性、二次稳定性和收缩性。此外，还设计了继承植物结构的鲁棒分布式滤波器。提出了保证鲁棒分布式滤波器存在的充分必要条件。最后，