In the purpose of making the consensus algorithm robust to outliers, consensus on the median value has recently attracted some attention. It has its applicability in for instance constructing a resilient distributed state estimator. Meanwhile, most of the existing works consider continuous-time algorithms and uses high-gain and discontinuous vector fields. This issues a problem of the need for smaller time steps and yielding chattering when discretizing by explicit method for its practical use. Thus, in this paper, we highlight that these issues vanish when we utilize instead Implicit-Explicit Method, for a broader class of networks designed by the blended dynamics approach. In particular, for undirected and connected graphs, we propose a discrete-time distributed median solver that does not suffer from chattering. We also verify by simulation that it has a smaller iteration number required to arrive at a steady-state.

中文翻译：

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通过隐式-显式方法获得的网络：离散时间分布式中值求解器

为了使共识算法对异常值具有鲁棒性，最近对中值的共识引起了一些关注。它适用于例如构建弹性分布式状态估计器。同时，现有的大部分工作都考虑了连续时间算法，并使用了高增益和不连续矢量场。这就产生了一个问题，即在实际使用中通过显式方法进行离散化时需要更小的时间步长并产生颤动。因此，在本文中，我们强调，当我们使用隐式-显式方法代替由混合动力学方法设计的更广泛的网络类别时，这些问题就会消失。特别是，对于无向图和连通图，我们提出了一种不受抖动影响的离散时间分布式中值求解器。