It has recently been shown that to stabilize an interval plant family with a first-order compensator is equivalent to stabilize only sixteen of the extreme plants. This paper aims at extending the above result to that with generalized compensators. Using a different approach from a previous paper it is shown that a generalized compensator robustly stabilizes an interval plant family if and only if it stabilizes thirty-two one-dimensional edges connecting extreme points of the given interval plant. No pagination in original publication.