On the genericity of stabilizability for time-delay systems

Conditions for the stabilizability of time-delay systems with incommensurable point delays by dynamic state feedback are known in the literature. In this paper it is shown that these conditions are satisfied generically. Although an algebraic approach is used to describe the class of all time-delay systems with point delays, the concept of genericity is formulated in a topological framework. In the metric space consisting of all parametrizations of time-delay systems, the subset of all stabilizable systems is an open and dense subset. The proof is given for the commensurable delay case first. It is shown that the incommensurable delay case is not significantly more difficult and that the same arguments prove also that systems with incommensurable time-delays are generically stabilizable.