Abstract: This paper focuses on the consensus problem of a class of heterogeneous multi-agent system mixed first agent with second agent as well as multiple time-varying delays. First, consensus protocol is proposed for the heterogeneous system. By system decoupling and model transformation, it decomposes the original system into several simple subsystems. Second, by employing the Lyapunov-Krasovskii stability theory, giving the system sufficient conditions to achieve the average consensus in the form of linear matrix inequalities. Third, it determines the compact admissible upper bounds of multiple delays by solving the feasible linear matrix inequalities. It also analyzes the impact of the delay derivative and the control gain on the upper bounds, it shows that the upper bounds are inversely related to the delay derivative, positively related to the control gain and are relatively small when the delay derivative is unknown. Finally, the result of numerical examples are presented to illustrate the availability of the theoretical results.

Key words: heterogeneous multi-agent, multiple delays, average consensus, Lyapunov stability theory, Linear Matrix Inequality（LMI）

摘要： 针对一类具有多变时延的一阶与二阶异构多智能体系统，研究了一致性问题。首先在异质系统中设计了一致性控制算法，通过将一阶、二阶系统重排和模型变换，使原系统分解成多个简单子系统；其次，利用李雅普洛夫稳定理论，分别在固定有向拓扑结构和切换有向拓扑结构下，以线性矩阵不等式的形式给出了系统达到平均一致的充分条件；再次，通过求解一组可行的线性矩阵不等式，得到了多时延的一个容许上界；然后讨论了时延导数和控制增益对时延容许上界的影响，得出了时延上界与时延导数和控制增益分别成正相关及反相关，时延导数未知时的时延上界相对较小的结论；最后的仿真结果表明了理论结果的有效性。

关键词: 异质多智能体, 多变时延, 平均一致性, 李雅普洛夫稳定性理论, 线性矩阵不等式