This article studies a decoupling cooperative control (DCC) with state feedback. It solves the output consensus problem on heterogeneous multiagent systems (MASs) over the input graph whose all nodes are reachable from the external reference signal. In light of the communication topology, the DCC forces each agent to reach a consensus on the given trajectory, which is from the reference signal of the common exosystem. Here, the output consensus problem is first equivalently converted into a stabilization one. Second the DCC involves a mapping <inline-formula> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula> of Laplacian matrix <inline-formula> <tex-math notation="LaTeX">${\mathcal{ L}}$ </tex-math></inline-formula>, i.e., every diagonal element of the Laplacian matrix is multiplied by a parameter <inline-formula> <tex-math notation="LaTeX">$d_{i}$ </tex-math></inline-formula>. <inline-formula> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula> moves Ger<italic>š</italic>gorin circles of <inline-formula> <tex-math notation="LaTeX">${\mathcal{ L}}$ </tex-math></inline-formula>. By the merit of <inline-formula> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula>, the equivalent stabilization problem is solved by the strictly positive real (SPR). In fact, the DCC is an approximate distributed decoupling control, when <inline-formula> <tex-math notation="LaTeX">$d_{i}$ </tex-math></inline-formula> is sufficiently large. In addition, under the framework of the DCC, the assignment problem of the dominant poles for each agent is also solved by inverse optimal regulator technology in this article. Finally, several simulation examples verify the effectiveness of our method.