Robust D stabilization of a polytope of matrices

The problem of stabilization of a polytope of matrices in a subregion D R of the complex plane is revisited. A new sufficient condition of robust D R stabilization is given. It implies the solution of an LMI involving matrix variables constrained by a non-linear algebraic relation. Some LMI relaxations are first proposed. Then, it is shown that a cone complementarity formulation of this condition allows us to associate an efficient iterative numerical procedure which leads to a low computational burden. This algorithm is tested on different numerical examples for which existing approaches in control literature fail.