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While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neurally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we will give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then we will give conditions under which the problem can be converted into a robust stabilization problem of an augmented system. Finally, we will present the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.