An exterior-point approach to the robust D-stability control problem

This paper treats the robust D-stability control against a parameter dependent uncertainty. It is well known that such robust control problems are difficult to be solved, because they become non-convex problems described by parameter dependent bilinear matrix inequalities (PDBMI´s). In this paper, we propose an exterior-point approach to the PDBMI problems such that a non-stabilizing controller can be used as an initial point. The feature of our approach is to produce a controller sequence from an infeasible region to a feasible one. Numerical example shows the efficiency of our approach.