In this paper, we propose output feedback and state feedback controllers for output regulation of linear heterogeneous multi-agent systems. We use a general model for the output regulation problem of linear multi-agent systems which accounts for a general directed and fixed communication graph, heterogeneity of the agents, an arbitrary number of inputs and outputs and both state and output feedback. First, we derive global and local sufficient conditions for the existence of local output feedback and local state feedback controllers. We show that both controllers have an Ho, criterion as a part of their sufficient conditions. Second, we design these controllers locally to insure those sufficient conditions. Third, for the case of output feedback, we show that the design procedure requires a feasible solution to the set of two LMIs and one non-convex algebraic constraint. We provide an existing algorithm to find a feasible solution to this problem. Fourth, for the case of state feedback we prove that the H-infinity criterion is satisfied if and only if there exists a feasible solution to an LMI. Moreover, we define an output regulation region such that selecting the state feedback coupling gain from this region ensures that the sufficient condition is always satisfied. (C) 2016 Elsevier Ltd. All rights reserved.