Robust Regulation with Adaptive Periodic Internal Models

In this paper, we consider the robust linear output regulation problem for minimum-phase systems driven by parameter-dependent periodic exosystems. A general methodology for construction of robust regulators for time-varying systems is not available, due to the absence of an equivalent version of the Cayley-Hamilton theorem. We show how a robust regulator can be easily constructed for minimum-phase plant models if appropriate observability conditions hold. The main result of the paper shows that a non-minimal realization of the resulting time-varying internal model is instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models. A key feature of the proposed solution lies in the fact that a persistence of excitation condition is not required for asymptotic regulation