Incorporation of unstructured uncertainty into the horowitz design method

Abstract

The Horowitz design method has long been known to yield closed loop systems that perform well for plants exhibiting structured or parametric uncertainty. Here it is shown that uncertain plants P(s) = P/sub nom/ (s) + (1 + M(s)) with the asymptotically stable and rational, so called unstructured uncertainty M(s), where IM(iw)jI < m(w) for all frequencies w, naturally fit into the Horowitz design framework. In particular, the realistic case of P(s) having structured uncertainty at low frequencies and unstructured uncertainty at high frequencies is treated. A theorem, giving necessary and sufficient conditions for the Horowitz method to work is presented, by which the interplay between plant knowledge and achievable closed loop specifications is clearly seen.