一类具有时滞和领导者的二阶多智能体系统的一致性

Consensus of a Class of Second Multi-agent Systems with Active Leader and Time Delay

研究了一类具有时滞和领导者的二阶多智能体系统在静态和动态拓扑网络中的一致性。首先运用代数图论描述此类多智能体系统的数学模型,然后借助于图的连通性质和平衡图代数性质,并结合Lyapunov泛函方法和矩阵不等式,得到系统达到一致性的充分必要条件,即当系统的参数满足β/α>γλ/2+1/λ,且时滞上界τ充分小时,在固定拓扑网络中领导者结点r全局可达与系统一致是等价的。对于切换拓扑情形的多智能体系统一致性有类似结论。

In this paper, we consider consensus problem of a class of second multi-agent systems with active leader and time delay in static and dynamic topology network. We first describe the mathematical model of the systems in term of algebraic graph theory. U- sing Lyapunov function method and the matrix inequality, we give the sufficient and necessary conditions ensuring that the system is consensus. That is, when system parameters satisfiesβα〉γλ2＋1λ and r is sufficiently small, then the system is consensus if onlyleader node r is globally reachable in G in a static fixed-topology network. For the case of the switching topology network, we havesimilar results.