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.