In this paper, the problem of minimum-energy control of linear systems determined in terms of two differential operators is investigated. By introducing the reduced-order inverse of the system discussed in this paper，we reveal that the input and output of the system are connected by a integro-differential operator. This operator is used to define the correspondence between the optimal controls and certain generalized splines. Finally，the formulas and the recursive algorithm，similar to those in [l]，for the optimal controls and the generalized splines are obtained.