Stability and Disturbance Propagation in Autonomous Vehicle Formations : A Graph Laplacian Approach

Recent works have combined tools from graph theory and control theory to derive stability criteria for vehicle formations. The formulation typically models information exchange between vehicles in a formation by using graph-theoretic tools. This work builds upon these ideas by studying the link between topology of these graphs and the dynamical behavior of a formation subject to disturbances. The problem is re-formulated by using Kronecker products. It is then shown how the Schur decomposition of the graph Laplacian matrix may be used to identify singular disturbance directions. The results we present may be used to simplify the design of robust decentralized controllers for large scale vehicle formations.