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. For this, two different topologies are introduced. One turns the parameter-space of all time-delay systems into a metric space. The other is a stronger, inductive limit topology. In both cases, stabilizability is called a generic property, it the subset of all stabilizable delay systems in an open and dense subset. First it is shown that this genericity result holds in the metric space of all time-delay systems. Using the inductive limit topology, it is possible to extend this result to a far more general class of stabilizability problems