This paper addresses the problem of bipartite consensus for discrete-time multi-agent systems with Markovian-jumping parameters under the influence of time-varying communication delay and actuator saturation. The main aim of this work is to propose an observer-based control protocol such that the bipartite consensus of the uncertain Markovian-jumping multi-agent system under consideration can be achieved. An undirected structurally balanced signed graph is utilized to describe the cooperative and antagonistic interaction among neighboring agents. Combining algebraic graph theory together with Lyapunov stability theory, a new set of sufficient conditions is derived by using Jensen’s inequality and Abel-lemma based finite sum inequality to achieve bipartite consensus. At last, a numerical example is provided with simulations to validate the effectiveness of the developed theoretical results.

本文解决了在时变通信延迟和执行器饱和的影响下具有马尔可夫跳跃参数的离散时间多智能体系统的二部共识问题。这项工作的主要目的是提出一种基于观察者的控制协议，以便可以实现正在考虑的不确定马尔可夫跳跃多智能体系统的两方共识。无向结构平衡有符号图用于描述相邻代理之间的合作和对抗交互。将代数图论与李雅普诺夫稳定性理论相结合，利用詹森不等式和基于阿贝尔引理的有限和不等式，推导出一套新的充分条件，以实现二部一致。最后，