Partitioning of relative sensing networks: A stability margin perspective

This paper studies partitioning a relative sensing network (RSN) of homogeneous dynamical sub-systems based on a stability margin criterion, where the RSN forms a network via the feedback channels. Here the main idea is to find a pair of partitioned networks such that their minimum stability margin is greater than all the other possible partitions’. To deal with this problem an exact method (EXACT) is first proposed which searches over all possible partitions and finds the best solution. Since the exact method is limited to relatively small-sized networks, the second method (GRT) is introduced to partition a so-called separable network (not strongly connected but being able to be partitioned into sub-networks each of which contains a globally reachable node) at a low-computational cost. In particular this second method guarantees that the partitioned networks have the stability margins equal or greater than the original network's. Extensive numerical simulations are carried out to investigate the efficacy of the proposed methods.