Abstract: We focuses on the group consensus problem of a class of first- and second-order heterogeneous multi-agent systems. First, we propose a static group consensus algorithm for the heterogeneous system with multiple time-varying delays. Second, by using stability theory and linear matrix inequality, we give the conditions that enable the heterogeneous multi-agent system to reach group consensus without delays and with communication and input delays respectively. Third, we determinethe upper bound of the input delay by solving the feasible linear matrix inequalities. The results show that the heterogeneous multi-agent system group consensus does not depend on communication delays. Finally, the simulation results illustrate the feasibility of the theoretical results.