Algorithms for computation of the total set of PID stabilizers based on decoupling of PID parameter space at singular frequencies are presented. Nonconvex stability regions are built up by convex polygonal slices. Two problems are thereby discriminated: (A) assertion of k (P)-intervals with stable polygons and (B) automatic detection of stable polygons for a fixed k (P). This paper includes solutions to both problems. The methods apply also for robust PID stabilization of a multi-model uncertainty. (c) 2006 Elsevier Ltd. All rights reserved.