This　paper　addresses　the　convergence　issue　of　first-order　and　second-order　PD-type　iterative　learning　control　schemes　for　a　type　of　partially　known　linear　time-invariant　systems.　By　taking　advantage　of　the　generalized　Young　inequality　of　convolution　integral,　the　convergence　is　analyzed　in　the　sense　of　the　Lebesgue-p　norm　and　the　convergence　speed　is　also　discussed　in　terms　of　Qp　factors.　Specifically,　we　find　that:　(1)　the　sufficient　condition　on　convergence　is　dominated　not　only　by　the　derivative　learning　gains,　along　with　the　system　input　and　output　matrices,　but　also　by　the　proportional　learning　gains　and　the　system　state　matrix;　(2)　the　strictly　monotone　convergence　is　guaranteed　for　the　first-order　rule　while,　in　the　case　of　the　second-order　scheme,　the　monotonicity　is　maintained　after　some　finite　number　of　iterations;　and　(3)　the　iterative　learning　process　performed　by　the　second-order　learning　scheme　can　be　Qp-faster,　Qp-equivalent,　or　Qp-slower　than　the　iterative　learning　process　manipulated　by　the　first-order　rule　if　the　learning　gains　are　appropriately　chosen.　To　manifest　the　validity　and　effectiveness　of　the　results,　several　numerical　simulations　are　conducted.　Copyright　(c)　2011　John　Wiley　and　Sons　Asia　Pte　Ltd　and　Chinese　Automatic　Control　Society