Analysis of large-time dynamics of the reachable sets to linear control systems

For linear time-invariant control systems under two types of constraints on control, geometric bounds and constraints on the total impulse of control, the asymptotic properties of the reachable sets are studied. The reachable sets can be represented as a product of a scaling matrix and a normalized reachable set. The scaling matrix is an elementary function of time, and, in the long run, the normalized reachable set approaches a convex body depending on time quasiperiodically in the impulsive case, and a fixed convex body in the geometric case.