引用本文: | 张庆杰,李远,朱华勇,等.l阶链式积分器型多智能体实现平均一致的时延相关LMI判据[J].国防科技大学学报,2011,33(5):83-90.[点击复制] |
ZHANG Qingjie,LI Yuan,ZHU Huayong,et al.LMI-based Delay-dependent Stability Criterion for Average Consensus of Multi-agent Systems with Lth-order Chain Integrator Dynamics[J].Journal of National University of Defense Technology,2011,33(5):83-90[点击复制] |
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l阶链式积分器型多智能体实现平均一致的时延相关LMI判据 |
张庆杰, 李远, 朱华勇, 沈林成 |
(国防科技大学 机电工程与自动化学院,湖南 长沙 410073)
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摘要: |
针对l阶链式积分器型多智能体平均一致性问题,给出联合连通拓扑条件下LMI表示的时延相关稳定判据。利用状态分解思想,将收敛条件转化为判断不一致系统零平衡点的稳定性;考虑存在多个时变通信时延的情况,采用构造公共的Lyapunov-Krasovskii泛函的方式来分析系统稳定性,为获得较低保守性判据,在主要结论中引入了自由权矩阵思想;最后,经过降阶处理并判断相应的LMIs可行解的存在性,可获得多智能体实现平均一致所允许的最大通信时延。数值实例和仿真实验表明方法的有效性。与已有文献相比,该稳定判据具有保守性低、求解形式简单、适用更广的时变时延范围等特点,对于分析和讨论复杂网络条件下多智能体平均一致性问题具有一定的指导意义。
〖HTH〗关键词:〖HTSS〗平均一致性;Lyapunov Krasovskii泛函;线性矩阵不等式;自由权矩阵;联合连通;时延相关稳定判据 |
关键词: 平均一致性 Lyapunov-Krasovskii泛函 线性矩阵不等式 自由权矩阵 联合连通 时延相关稳定判据 |
DOI: |
投稿日期:2011-03-02 |
基金项目:国家省部资助项目(A2820080247,6138101001) |
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LMI-based Delay-dependent Stability Criterion for Average Consensus of Multi-agent Systems with Lth-order Chain Integrator Dynamics |
ZHANG Qingjie, LI Yuan, ZHU Huayong, SHEN Lincheng |
(College of Mechatronics Engineering and Automation, National Univ. of Defense Technology, Changsha 410073, China)
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Abstract: |
For the average consensus of multi-agent systems with lth-order chain integrator dynamics, it is important to build the LMI-based delay-dependent stability criterion with jointly-connected topologies. Using the idea of state decomposition, the condition was converted into verifying the stability of zero equilibrium of disagreement system. Considering multiple time-varying communication delays, common Lyapunov-Krasovskii functional was employed to analyze the stability of zero equilibrium. In order to relax the conservativeness, Free-weighting Matrices method was employed in the main results. After matrix order-reduced treatment, the tolerant upper bounds on communication delays were obtained through solving feasible linear matrix inequalities (LMIs). Numerical examples and simulations were presented to demonstrate the effectiveness of the proposed method. Different from the existing literature, the proposed stability criterion was characterized by lower conservativeness, simple formation of the solution, and wide range of time-varying delays. It can be applied to instruct the analysis and discussion of the average consensus of multi-agent systems with complicated communication conditions. |
Keywords: average consensus Lyapunov-Krasovskii function Linear Matrix Inequlities(LMI) free-weighting matrices jointly-connected delay-dependent stability criterion |
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