This paper formulates a robust output regulation problem for a linear time-invariant system with uncertain parameters whose controlled output may be different from the measurement output. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers that achieve robust output regulation; each of them consists of a proportional plus integral regulator and a proportional plus integral observer. It turned out that the regulator is a state feedback controller that achieves output regulation and the observer is an unknown input observer for a system with either fictitious exogenous input or fictitious controlled output.