Realization of a frequency response: A generalized μ approach

The aim of this paper is to find a fixed structure transfer matrix, whose dynamics (i.e. whose poles) are not a priori fixed, and whose frequency response is the closest as possible to a target one. This non convex optimization problem is recast into a generalized μ problem. A generalized n lower bound is proposed, which provides an a priori suboptimal solution (i.e. a local minimum), namely a transfer matrix whose frequency response fits to a large extent the target response. A generalized μ upper bound is used to quantify the degree of optimality of the result (i.e. a reliable estimate of the gap between the local minimum and the global one). An example illustrates the effectiveness of the approach.