  In this paper, we proposed an procedure to construct the completion of the
integrable system by adding a perturbation to the generalized matrix problem,
which can be used to continuous integrable couplings, discrete integrable
couplings and super integrable couplings. As example, we construct the
completion of the Kaup-Newell (KN) integrable coupling, the
Wadati-Konno-Ichikawa (WKI) integrable couplingsis, vector
Ablowitz-Kaup-Newell-Segur (vAKNS) integrable couplings, the Volterra
integrable couplings, Dirac type integrable couplings and NLS-mKdV type
integrable couplings.
