Dynamical Network Partitioning: A Stability Margin Perspective

This paper studies partitioning homogeneous dynamical networks based on the stability margin of networked control system. Here the main idea is to find a pair of partitioned networks that their minimum stability margin is greater than all the other possible partitions. To deal with this problem three methods have been introduced. At first an exact method (EXACT) is proposed which goes over all the possible partitions and finds the best solution. The second method is a heuristic method (HEU) that aims to reduce the computational burden of the first approach using the frequency at which the stability margin of the original network is attained, instead of all the possible frequencies. Since the first and second methods are limited to relatively small-sized networks, the third method (GRT) is introduced to partition arbitrarily large networks while maintaining a low-computational cost. In particular the third method guarantees that the partitioned networks have stability margins equal or greater than the original network.