Output regulation in the presence of quadratically bounded parameter uncertainties

Abstract

The problem of robust output regulation is studied for a class of parameter uncertain systems under unity output feedback control. The objective is tracking of the desired reference trajectory in the presence of the disturbance, both generated by a common exosystem. Because of the anti-stability of the exosystem and potentially unbounded reference trajectory, the output tracking error is employed as the measurement signal and used as the input to the feedback controller. The method of p-copy of the internal model is utilised to augment the plant dynamics. Assuming that the output regulation condition is satisfied for all the parameter uncertainties, it is shown that the problem of robust output regulation is equivalent to the problem of robust output stabilisation. Furthermore, for quadratically bounded parameter uncertainties, an application of the notion of the quadratic stability leads to H ∞ -based robust control, and the maximum allowable uncertainty bound can be computed, below which the robust output regulation can be achieved.