Abstract
This paper introduces a data-driven approach for computing reduced-order models of leader-less discrete-time multi-agent systems while preserving stability and synchronisation properties. Unlike existing methods, which typically rely on the high-order model to be reduced, the proposed approach does not require a prior model of the system but instead leverages data directly collected from the system itself. The contributions are threefold. First, sufficient conditions on the individual agent for stability and synchronisation of a discrete-time multi-agent system utilizing a model-based algebraic Riccati inequalities (ARI) are provided. However, without a known system model, direct verification of the ARI is infeasible to perform. Therefore, as the second contribution, scenarios where the system model is unknown are addressed by establishing necessary and sufficient conditions for stability and synchronisation in terms of data-driven linear matrix inequality (LMI). This allows the verification of both properties solely through the collected data. Finally, the computation reduced-order models based on the extremal solutions of the ARI or LMI is provided, resulting in stabilised and synchronised systems with lower dimensionality. The effectiveness and good performance of the proposed approach is demonstrated by a simulation study involving a network of aircraft models.