On Set Stability of Finite-Field Networks

In this brief, the set stability problem for finite-field networks (FFNs) is investigated. This study covers stability and consensus as special cases. For the set stability of a given set, we provide several necessary and sufficient conditions on the network topology, weights, and the largest invariant subset (LIS) included in the set, respectively. Particularly, we apply abstract algebraic method to determine a special case, which can degenerate into stability and consensus. Additionally, transient period of FFNs are estimated by means of probability and invariant subsets.