On the best achievable SISO simultaneous performance

Best achievable SISO simultaneous performance is formulated as a minimum distance problem from a point to a nonconvex set defined by interpolation and simultaneous stabilization constraints. It is shown that constraint truncation and underestimation and subsequent use of duality theory lead to a bilevel program whose solution can be found through iteration between a convex and a linear program. The proposed procedure is shown to identify best achievable simultaneous performance as the limit of a nondecreasing sequence of rigorous lower bounds.