Robust Stabilization Based on Topological Connectedness

In this paper we investigate under what conditions the stabilizability of a given plant G(¿o,s) implies the stabilizability of every plant G(¿,s) {G(¿,s) | ¿ ¿}. These new general conditions for robust diagonal stabilization of a plant set are based on topological connectedness. When the conditions of our main theorem are satisfied, we say that the set {G(¿,s)} is topologically path connected. It turns out that the path connectedness of {G(¿,s)} is a necessary condition for the robust stabilization of the set but no constructive or easily comparable criterion for checking path connectedness has until now been put forth.