On generic properties of linear systems: An overview

The topological space of linear, time-invariant systems is considered. A properly of linear systems is called generic if the systems equipped with this property occupy an open and dense subspace of the space of systems. Several generic properties of linear systems are reviewed, including controllability, observability, invertibility, structural stability, as well as some topological properties of orbits of the feedback group. A new estimate for the number of orbits of the feedback group is produced, and a differential geometric proof of the existence of generic controllability indices is given.