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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 network constraints such as multiple time-varying delays, finite energy perturbations, and uncertain topological structures, a delay-dependent criterion for robust consistency of multi-agent systems is given.Firstly, by using state decomposition The original problem is transformed into discussing the robust stability of the inconsistent vector system. Then, considering the time-varying delays and dynamic topologies, the robust stability of the system is analyzed by constructing the Lyapunov-Krasovskii functional and the free-matrix method Finally, based on the idea of solving the cone complement problem, nonlinear minimization of NLMI criterion is performed to obtain the LMI stability criterion with low conservativeness and easy solution. Numerical examples and simulation results verify the validity of the proposed criterion.