Abstract
This paper is concerned with the approximate controllability of two systems by means of a common input function.In the paper,the two systems are considered to be infinite-dimensional and one of them to be a Riesz-Spectral system.In this case,it is shown that if both systems are exactly controllable in time T_0 and the system generators have no common eigenvalues,then they are simultaneously approximately controllable in any time TT_0.In addition,for special control operators,if one system(A_1,B_1) is approximately controllable and the other(A_2,A_2) is exactly controllable in time T_0,and the spectral sets of the two system generators satisfy the conditionσ(A_2)ρ_∞(A_1),then they are simultaneously approximately controllable in some time T0.Finally,some applications of the obtained results are given and it is proved that the time at which the systems are simultaneously approximately controllable is optimal.
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