On the robustness of discrete iterative learning control system against initial state error

The robustness of discrete iterative learning controller a-gainst initial state state error for discrete-time plant is investigated in this paper. When the initial state remains fixed for each iteration but is different from the desired one, it is shown that the output will converge to a trajectory which is the same as the desired one except the initial point for a traditional D-type discrete iterative learning controller. A modification of the D-type algorithm is then proposed to improve the tracking speed while retains the same learning performance against the initial state error. For the case of variable initial error condition, it is also shown that the tracking error is guaranteed to be bounded and the bound on tracking error in the final iteration can be tuned by the parameter of this proposed modified algorithm.