Stability analysis of digital repetitive control systems under time-varying sampling period

Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.