For a large class of robustness problems with uncertain pa.rameter vector q confined to a box Q, there are many papers providing results along the following lines: The desired performance specification is robustly satisfied for all q E Q if and only if it is satisfied at each ver-t8ex pi of Q. Since the number of vertices of Q explodes combinatorically with the dimension of q , the computation associated with the implementation of such results is often intractable. The main point of this paper

more »

... s to introduce a new approach to such problems. To this end, the definition of approximate feasibility is introduced, and the theory which follows from this definition is vertex-free.