This paper provides convergence/stability criteria for universal adaptive high-gain iterative learning control systems based on the use of the current trial feedback for a class of linear MIMO state space systems. Weak and strong (norm) convergence of the tracking error sequences {e/sub k/}/sub k/spl ges/0/ to zero in L/sub 2//sup m/(0,T) is analysed. This perfect tracking is is also achieved with convergence of the adaptive control K/sub k/ to a limit gain K/sub /spl infin// guaranteed in the proposed gain-update laws.