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In this paper, the consensus problem of descriptor multi-agent systems is considered. Each agent’s dynamics is given in the general form of a continuous-time linear descriptor system, and the communication topology among the agents is assumed to be directed in fixed topology case and balanced in switching topology case, respectively. Three kinds of distributed observer-based consensus protocols are proposed to solve the descriptor multi-agent consensus problem. Multi-step algorithms are provided to design the gain matrices and coupling constants involved in the protocols. The design approach is based on the generalized Riccati equation, and Lyapunov stability theory. Some sufficient consensus conditions are established to guarantee that the descriptor multi-agent system achieves consensus under the directed fixed topology and balanced switching topology. Furthermore, the state variable feedback consensus problem and the observer-based consensus problem with a desired decay rate are discussed. Finally, a simulation example is provided to illustrate the obtained results.

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