The $H_{\infty }$-consensus control problem is studied for a class of multi-rate multi-agent systems based on the outlier-resistant observers. To reduce the measurement cost and save the bandwidth resource, the multi-rate strategy is introduced to regulate the sampling rates of each agent. Next, the outlier-resistant observer is constructed for each agent, where the specific saturation function is introduced to restrain the adverse effect from the possible outliers. Then, the distributed consensus controller is designed for each agent by utilizing the available information from its own observer and its neighboring agents. The aim of this paper is to design the gain parameters for each agent such that the resulting augmented system can achieve the asymptotic stability as well as the $H_{\infty }$ disturbance attenuation constraint when encountering the possible measurement outliers. The sufficient condition is derived to guarantee the existence of the gain parameters, which are calculated by solving a semi-positive definite problem. Finally, an illustrative simulation example is employed to validate the feasibility of the consensus control scheme.

这 $H_{\infty }$研究了一类基于抗异常观察者的多速率多智能体系统的共识控制问题。为了降低测量成本和节省带宽资源，引入了多速率策略来调节每个代理的采样率。接下来，为每个代理构建抗异常值观察器，其中引入特定的饱和函数以抑制可能的异常值的不利影响。然后，通过利用来自其自己的观察者及其相邻代理的可用信息，为每个代理设计分布式共识控制器。本文的目的是为每个智能体设计增益参数，使得所得的增强系统能够实现渐近稳定性以及$H_{\infty }$遇到可能的测量异常值时的干扰衰减约束。推导出了保证增益参数存在的充分条件，该增益参数是通过求解一个半正定问题来计算的。最后，一个说明性的模拟例子被用来验证共识控制方案的可行性。