  In this paper, we investigate tracking control of heterogeneous multi-agent
systems under Denial-of-Service (DoS) attacks and state quantization. Dynamic
quantized mechanisms are designed for inter-follower communication and
leader-follower communication. Zooming-in and out factors, and data rates of
both mechanisms for preventing quantizer saturation are provided. Our results
show that by tuning the inter-follower quantized controller, one cannot improve
the resilience beyond a level determined by the data rate of leader-follower
quantized communication, i.e., the ceiling effect. Otherwise, overflow of
followers' state quantizer can occur. On the other hand, if one selects a
"large" data rate for leader-follower quantized communication, then the
inter-follower quantized communication determines the resilience, and further
increasing the data rate for leader-follower quantized communication cannot
improve the resilience, i.e., the bottleneck effect. Simulation examples are
provided to justify the results of our paper.
