Guaranteed robust control of unstable systems by using approximated models

Some preliminary results regarding the design of low-order compensators for unstable plants are presented. With the proposed approach it is possible to compute the compensator which robustly stabilizes a given unstable plant, after approximating the system with a reduced-order model whose only constraint is retaining the same number of unstable poles as the original one. The conditions for obtaining a low order uncertainty function are also given. The solution to the problem can be obtained by using a min-max approximation approach. The proposed strategy is illustrated by a numerical example