Consensus analysis for a class of mixed-order multi-agent systems with nonlinear consensus protocols

The consensus problem for a class of mixed-order multi-agent systems is investigated in this paper, where the multi-agent system is composed of first- and second-order dynamic agents. Firstly, consensus protocols are proposed for solving the finite-time consensus problem for mixed-order multi-agent systems. By employing the finite-time stability theory and LaSalle's invariance principle, some sufficient conditions for finite-time consensus are given for multi-agent systems with directed communication topologies. Then, a class of nonlinear consensus protocols are given to solve the asymptotic consensus problem for mixed-order multi-agent systems. In addition, an invariant quantity is introduced to specify the expressions of the final consensus states when asymptotic consensus is reached. Finally, a simulation example is provided to demonstrate the effectiveness of the theoretical results.