The aggregation on linear large-scale dynamic systems is examined in this paper and a "two-step" approach is proposed. In this procedure, the aggregated system consists of two subsystems. The first subsystem represents aggregation through the retainment of dominant eigenvalues of the original system, leading to a first approximation of the desired output of the original system. The purpose of augmenting it with a second subsystem is to provide an estimation of the error on the first approximation, thus permitting a second correction to the output approximation and resulting in an output approximation of greater accuracy. Optimization techniques are discussed for the determination of unknown parameters in the aggregated system. These techniques use minimization principles of certain suitable performance indices and are developed for both single input-single output and multiple input-multiple output system. Numerical examples illustrating these procedures are given and the results are compared with those obtained using existing methods. Finally, a pharmacokinetics problem is studied from the aggregation point of view.