Input Delay Compensation in Multi-Agent Systems via Piecewise Constant Control

We consider a multi-agent system with time-invariant topology containing several agents governed by similar linear time-invariant ODEs with constant delay in actuation. Piecewise constant (PWC) control with sampling time larger than the delay value is applied. Assuming the delay-free version of the system can be brought to consensus by the PWC feedback, we design a predictive PWC feedback achieving consensus in the system with delayed input. During prediction, PWC structure is employed to determine future input to the system from its past output. This input is then used to predict the future state and compensate for the delay.