An efficient algorithm for the construction of ℓ1 uncertainty model sets

Robust control techniques require the construction of uncertainty model sets. When dealing with unstructured norm-bounded uncertainties, it is important that the size of the uncertainty set is minimized, so that robust performances can be enhanced. This paper addresses the problem of constructing the minimum ℓ₁ uncertainty model set containing a finite set of assigned models. The problem is formulated as a conditional Chebyshev center problem and an efficient algorithm for its solution is proposed. The algorithm converges in a finite number of steps and is able to deal with large size problems in reasonable time.