Networks Obtained by Implicit-Explicit Method: Discrete-Time Distributed Median Solver

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