Robust formation control of uncertain linear multi‐agent systems in presence of time‐delay using output information

A major challenge in multi‐agent formation is the issue of delay and uncertainty. This article investigates a robust formation control problem for linear multi‐agent systems with input delay and model uncertainty. The strategy adopted by an agent in the system aims to predict the delayed state using output information from neighboring agents over a fixed communication network and generate the control input from the predictor output. The predictor is employed using the finite spectrum assignment (FSA) technique. The overall strategy leads to a unified framework representation, and the multi‐agent formation control problem is simplified to a closed‐loop stability problem for an agent. The overall problem comes down to deciding two feedback gains: predictor gain and controller gain. For a perfect plant model, any choice of stabilizing gains can achieve formation. But when agent models are uncertain, the gains need to be derived from the solutions of linear matrix inequalities (LMIs) containing network information and delay. LMIs are obtained from the bounded real lemma and the gains obtained from the solution guarantee to maximize the H∞$$ {H}_{\infty } $$ norm bound of allowable perturbation, modeled as additive uncertainty, for a known delay size. Further, since the FSA technique is sensitive to discretization, a digital implementation of the overall scheme is elaborated, which may help to debug stability issues in the implementation process. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed ideas.