On computation of the total set of robust discrete-time PID controllers

The problem of finding the set of all multi-model robust PID and three-term stabilizers for discrete-time systems is solved in this paper. The method uses the fact that decoupling of parameter space at singular frequencies is invariant under a linear transformation. The resulting stable regions are composed by convex polygonal slices. The design problem includes the assertion of intervals with stable polygons and the detection of stable polygons. This paper completes the solutions to both problems.