Adaptive backstepping repetitive learning control for discrete-time periodic systems

In this paper, the problem of adaptive backstepping repetitive learning control is addressed for a class of periodically time-varying discrete-time strict-feedback systems. A repetitive learning least squares algorithm is applied for parameter estimation, where the lower bound for the control gain is introduced to avoid the potential singularity. An iteration-domain key technical lemma is given for the purpose of performance analysis, which is a slight modification of the key technical lemma used for analysis of discrete adaptive systems. It is shown that the zero-error convergence can be achieved as the iteration increases, while the variables of the closed-loop system undertaken are bounded.