A Distributed PID-like Consensus Control for Discrete-time Multi-agent Systems

The problem of discrete-time multi-agent systems governed by general MIMO dynamics is addressed. By employing a PID-like distributed protocol, we aim to solve two relevant consensus problems, namely the leaderless consensus under disturbances and leader-follower under time-varying reference state ones. Sufficient conditions for stability as well as two LMI approaches to tune the controller gains are provided. The latter are either based on a H-infinity formulation of the problem or on fast response to a reference exogenous signal. Numerical simulations give some insight of which tuning should be considered according to the problem addressed.