Simultaneous scaling for MIMO controller certification

We consider methods for the computation of; maximal MIMO stability margins b_pc, minimal V-gap metrics zeta_v, and the maximal difference between these two values, through the use of scaling and weighting functions. We propose simultaneous scaling selections that maximize the generalized stability margin and minimize the V-gap. The minimization of the V-gap by scaling involves a non-convex optimization. We modify the XY-centering algorithm to handle this non-convexity. This is done for applications in controller certification, where the experimentally tested performance of one controller is used to provide guarantees on other controllers´ performance without the need for additional tests.