Controllability of impulse controlled systems of heat equations coupled by constant matrices

Abstract

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 q(A,B) different control instants 0<τ1<τ2<⋯<τq(A,B)<T, provided that τq(A,B)−τ1<dA, where dA≜min⁡{π/|Imλ|:λ∈σ(A)} and q(A,B)≤n. We also show that in general, such systems are not null controllable.