On avoiding vertexization of robustness problems: the approximate feasibility concept

For a large class of robustness problems with uncertain parameter 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 ε Q if and only if it is satisfied at each vertex qⁱ of Q. Since the number of vertices of Q explodes combinatorially with the dimension of q, the computation associated with the implementation of such results is often intractable. The main point of this paper is 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