This paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair (A, B) of constant matrices. We present a necessary and sufficient condition for the approximate controllability, which is exactly Kalman's controllability rank condition of (A, B). We prove that when such a system is approximately controllable, the approximate controllability over an interval [0, T ] can be realized by adding controls at arbitrary n different control instants 0 < τ 1 < τ 2 < · · · < τ n < T , provided that τ n − τ 1 < d A , where d A min{π/|Imλ| : λ ∈ σ(A)}. We also show that in general, such systems are not null controllable.
In REF , the authors studied the controllability for the system:
Controllability of impulse controlled systems of heat equations coupled by constant matrices
Journal of Differential Equations
Mathematics