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 n different control instants 0<τ_1<τ_2<\cdots<τ_n<T, provided that τ_n-τ_1<d_A, where d_A=\min\{π/|Im λ| : λ\in σ(A)\}. We also show that in general, such systems are not null controllable.