In this paper, we address the problem of full-information output regulation for linear systems subject to non-periodic non-smooth exogenous signals generated by explicit-form models. We study the steady-state response of the system obtained by the interconnection of the linear system, the explicit-form exogenous system, and a time-varying state-feedback controller. We provide solutions in the form of regulator equations and then study the solvability conditions by separating the analysis in two cases, namely one without feedforward term and with continuous exogenous signals, e.g. triangular waves, and one with a feedforward term and discontinuous exogenous signals, e.g. square waves. We finally illustrate the results by means of two examples.