An analytic characterization of a stabilizing feedback for LTI plants

The characterization of all stabilizing controllers via the Youla Parameterization requires prior knowledge of one stabilizing feedback. This task is trivial in the case of stable plants. In the unstable case, one needs to use a suitable design technique to obtain such a stabilizing controller. The resulting controller is usually not an explicit function of plant dynamical features. In this paper, we propose a stabilizing controller design such that the sensitivity function can be expressed as an explicit function of the non-minimum phase zeros, time delays, and unstable poles of the plant (and their directions in the multiple-input multiple-output case). These dynamical features are known to impose fundamental limitations on control performance. The results in this paper highlight their relevance since they are shown to be the minimum information required to build a stabilizing controller.