In　this　paper,　a　conventional　PD-type　iterative　learning　control　strategy　for　linear　time-invariant　system　to　track　unique　desired　trajectory　is　studied.　In　the　study,　the　convergence　of　the　iterative　learning　updating　law　is　analyzed　in　the　sense　of　Lebesgue-p　norm　by　means　of　Hausdorff-Young　inequality　of　convolution　integral.　In　the　analysis,　it　is　shown　that　the　convergence　property　depends　on　not　only　the　derivative　learning　gain　but　also　the　proportional　learning　gain.　The　validity　of　the　conclusion　and　the　effectiveness　of　the　proposed　learning　strategy　are　exhibited　by　numerical　simulations.