This paper presents analysis of number of steps required for the consensus in a leader-following discrete multi-agent system (DMAS) with discrete-time sliding mode protocols designed by Gao’s reaching law and power rate reaching laws. The DMAS is configured for communication with a fixed, undirected graph topology having one leader and other agents as followers. The sufficient condition for global stability is established using the Lyapunov function in both the cases. The efficacy of both the protocols is compared in simulation for number of steps required for the consensus of a homogeneous multiple two degree of freedom helicopter systems where the pitch angle and its velocity and yaw angle and its velocity are used for consensus. The simulation results reveal that the consensus performance due to protocol with power rate reaching law outperforms the protocol with Gao’s reaching law.

本文介绍了根据高氏到达定律和电费率到达定律设计的具有离散时间滑模协议的领导者跟随离散多代理系统（DMAS）中达成共识所需的步骤数。DMAS配置为与具有一个领导者和其他代理作为跟随者的固定，无向图拓扑通信。在这两种情况下，都使用Lyapunov函数为全局稳定性建立了充分条件。在仿真中比较了两种协议的有效性，以求出均质多个二自由度直升机系统的共识所需的步骤数，其中俯仰角及其速度，偏航角及其速度用于达成共识。