Possibilistic robust control for fuzzy plants: controlling performance degradation

One of the main problems of classical robust control approaches is that if a set of specifications are not fulfilled for a family of plants being considered, they must be relaxed. However, not all the plants in the family will be equally possible in practice. In this paper, a fuzzy set in a linear plant space will be used to associate a possibility to each member in the family. Then, a controller will be designed so that a fuzzy set of specifications is achieved. The core of this set will define the hard specifications to be achieved by the most possible plants, while the support will represent the minimum specifications required to the whole family of plants. Intermediate cuts define how performance is allowed to degrade. Several design methodologies are presented.