Robust Stabilization Based on Topological Connectedness

In this paper we investigate under what conditions the stabilizability of a given plant G(α o ,s) implies the stabilizability of every plant G(α,s) {G(α,s) | α ϵ Ω}. 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(α,s)} is topologically path connected. It turns out that the path connectedness of {G(α,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.