多智能体系统实现鲁棒一致的时延相关稳定判据

Delay-dependent stability criteria for robust consensus of multi-agent systems

考虑存在多个时变时延、有限能量扰动以及时变拓扑结构不确定等网络约束条件,给出了多智能体系统实现鲁棒一致性的时延相关稳定判据.首先,利用状态分解将原问题转化为讨论不一致向量系统的鲁棒稳定性;然后,考虑到多个时变时延和动态拓扑,采用构造Lyapunov-Krasovskii泛函的方式分析系统鲁棒稳定性,并利用自由权矩阵方法获得关于非线性矩阵不等式(NLMI)的可行解判据;最后,借鉴求解锥补问题的思想,对NLMI判据进行非线性最小化处理,以得到保守性低、易于求解的LMI稳定判据.数值实例和仿真结果均验证了所提出判据的有效性.

Considering the network restrictions such as multiple time-varying delays, disturbances with limited energy and time-varying topologies uncertainties, the delay-dependent stability criteria for robust consensus of multi-agent systems are proposed. Firstly, by using the idea of state decomposition, the condition for guaranteeing robust consensus is converted into verifying the robust stability of the disagreement systems. Considering multiple time-varying delays and switching topologies, Lyapunov-Krasovskii functional is constructed to analyse the robust stability. By using free-weighting matrices（FWM） method, the stability criteria can be obtained through solving the corresponding feasible nonlinear matrix inequality nonlinear matrix inequality（NLMI）. Finally, according to solving cone complementarity problem, nonlinear minimization is employed to obtain the LMI criteria with lower conservativeness and be solved easily. Numerical examples and simulation results show the effectiveness of the proposed criteria.