含时延约束的多智能体系统二分一致性

针对多智能体系统中信息交互存在通信时延这一约束，在无向符号图拓扑结构下分别研究了含固定时延和时变时延的一阶多智能体系统二分一致性问题。通过设计相应的控制协议，使得该系统收敛到两个模值相同但符号不同的状态。在稳定性分析中，利用广义Nyquist准则的方法，得到含固定时延多智能体系统实现二分一致性的充分条件；对含时变时延系统构造包含三重积分项的Lyapunov函数，利用积分不等式和线性矩阵不等式理论，并结合自由矩阵的方法得到含时变时延多智能体系统实现二分一致性的充分条件。最后，数值仿真验证了所得结论的有效性和正确性。

Bipartite consensus for multi-agent systems subject to time delays

The aim of this paper is to consider the practical constraint of interaction network associated with multi-agent systems (MASs) subject to communication delay, the bipartite consensus seeking is investigated for the first-order MASs with fixed time-delays and time-varying delays over an undirected signed graph, respectively. To solve the concerned problems, the corresponding algorithms oriented for fixed time-delays or time-varying counterpart are proposed. In other words, the consensus is achieved within each subgroup during evolution, in which the state of each subgroup will converge to the same modulus but different symbol. Sufficient condition of bipartite consensus for the interaction network of MASs suffered from fixed time-delays can be obtained by the use of the generalized Nyquist criterion; Furthermore, based on the tools of integral inequality and linear matrix inequality, the sufficient condition for the case of bipartite consensus for the interaction network of MASs with time-varying delays also can be derived through constructing a reasonable Lyapunov function with triple integral term. Numerical simulations are provided that demonstrate the effectiveness of our theoretical results.