  For iterative learning control (ILC), one of the basic problems left to
address is how to solve the contradiction between convergence conditions for
the output tracking error and for the input signal (or error). This problem is
considered in the current paper, where the robust convergence analysis is
achieved for ILC systems in the presence of nonrepetitive uncertainties. A
system equivalence transformation (SET) is proposed for ILC such that given any
desired reference trajectories, the output tracking problems for general
nonsquare multi-input, multi-output (MIMO) systems can be equivalently
transformed into those for the specific class of square MIMO systems with the
same input and output channels. As a benefit of SET, a unified condition is
only needed to guarantee both the uniform boundedness of all system signals and
the robust convergence of the output tracking error, which avoids causing the
condition contradiction problem in implementing the double-dynamics analysis
approach to ILC. Simulation examples are included to demonstrate the validity
of our established robust ILC results.
