Limit Behavior of Reachable Sets of Linear Time‐Invariant Systems with Integral Bounds on Control

In this paper, a linear dynamic system is considered under L p ‐constraint on control. We establish the existence of the limit shape of reachable sets as time goes to infinity. Asymptotic formulas are obtained for reachable sets and their shapes. The results throw a bridge between the cases of geometric bounds on control and constraints on the total impulse of control, and create a unified picture of the structure of the limit shapes of reachable sets.