Approximation of discrete-time systems with delay: application to multi-agent systems

The paper presents a novel approximation method for discrete-time Multi-Agent System (MAS)s with communication delay. The applied approximation method was initially developed for a class of infinite-dimensional homogeneous or-dinary linear Volterra difference systems. First, we extend this approximation to non-homogeneous systems. Second, based on this approximation, we have shown that discrete-time MAS with communication delay and small gains is asymptotically equivalent to a MAS without communication delay. We give an algorithm to compute the delay-free MAS model and we have analysed its properties. Simulations are presented to show the applicability of the proposed approximation approach.