Robust controller synthesis with unstable weights

In this paper we consider the problem of nominal controller synthesis with unstable weights. This problem turns out to be very useful in a `μ-like' synthesis algorithm for the systematic design of robust controllers with a general linear fractional dependence on the uncertainties. Such algorithms all rely on a suitable factorization of the involved scalings, which frequently causes numerical ill-conditioning in computations. In this paper, we show how to avoid any such factorizations. If compared to the existing approaches, this leads to a drastically simplified and numerically improved synthesis algorithm for the systematic design of robust controllers.