Effects of initial input on stochastic discrete-time iterative learning control systems

This paper deals with the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to random disturbances varying from iteration to iteration. It demonstrates that the convergence of both expectation and variance of the tracking error depends heavily on the selection of initial input. Based on the super-vector approach, effects of initial input on error convergence are discussed by developing some statistical expressions, and time-domain conditions are provided for both asymptotic stability and monotonic convergence of the ILC process. Furthermore, using properties of the block Topelitz matrices, it shows that the linear matrix inequality (LMI) technique can be applied to describe the convergence conditions regardless of the system relative degree, and formulas can be given for the control law design simultaneously. Some simulation tests are proposed finally to illustrate the theoretical results.