This paper is concerned with cooperative output regulation of heterogeneous multi-agent systems. Agents are allowed to be heterogeneous general linear time-invariant systems and the communication graph is not restricted to the acyclic type. New distributed state-feedback controllers with extra scalar parameters are constructed. A global sufficient solvability condition is first derived and simplified stability conditions for closed-loop poles in a specified region are then obtained in terms of an H_∞-type performance of local sub-systems coupled through a matrix associated with the graph. Linear matrix inequality conditions are further presented for allocating the H_∞-type performance levels and designing controllers for each sub-system. A numerical example is presented for illustrating the advantages of the proposed design method. Both continuous- and discrete-time multi-agent systems are investigated in a unified framework.