Consensus of discrete‐time double‐integrator multi‐agent systems with velocity and input constraints

Abstract This article addresses the consensus problems of the discrete‐time double‐integrator multi‐agent systems (MASs) with velocity and input constraints over an undirected graph. First, we design a distributed consensus protocol and provide the selection criterion for the control gain. Based on Lyapunov's direct method and LaSalle's invariance principle, it is proved that, under the appropriate initial velocity conditions, consensus of the closed‐loop systems is achieved with both velocity and input strictly constrained within the given bounds. Second, we extend the above result to the scaled consensus case, and the scaled consensus is ensured using the proposed control algorithm. Finally, some simulations are presented to validate the developed theoretical findings.