Constrained Controllability of Linear Impulse Differential Systems

We consider the following linear impulse differential control system {x = A(t)x Δx = B_kx(t_k) + Cku_k t ≠ t = t_k where the control sequences {uk} belong to some set of admissible controllers that is restricted either by norm or by range. We then give a necessary and sufficient condition for global null controllability of time-varying systems and some sufficient conditions for global null controllability for time-invariant systems with special structures.