Semi-Global Consensus of Multi-Agent Systems by Fully Distributed Energy-Constrained Linear Protocols

This work addresses the leader-following consensus problem for linear multi-agent systems subject to prescribed energy limitations over general directed communication networks, considering both continuous-time and discrete-time frameworks. For the continuous-time case, a distributed linear control protocol is developed by integrating a novel distributed observer with the solution of a parametric Lyapunov equation (PLE). Using key properties of the PLE and Lyapunov stability theory, the semi-global leader-following consensus is guaranteed under any predefined energy constraints. In parallel, a discrete-time protocol is also designed, and its stability is established by using the discrete-time parametric Lyapunov equation. A salient feature of the proposed protocols is that they eliminate the need for any global knowledge of the directed communication network (specifically, eigenvalues of the Laplacian matrix), thus enabling consensus over directed graphs containing a spanning tree rooted at the leader, with any number of agents, under energy constraints. Finally, two simulation studies are conducted to corroborate the theoretical findings.