Robust state feedback D stabilization via a cone complementary algorithm

The problem of stabilization of a polytope of matrices in a sub-region 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 nonlinear algebraic relation. A cone complementarity formulation of this condition allows 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.