Gain-Scheduled Consensus of Multi-Agent Systems Over Graphs Described by Parameter-Varying Laplacians

This paper addresses the design of a gain-scheduled consensus protocol for multi-agent systems (MASs). Unlike conventional approaches that restrict the graph Laplacian to be fixed or switching matrices representing distinct topologies, we propose allowing it to vary as a function of a time-varying parameter vector available in real-time. For this situation, we derive design conditions that ensure convergence of the synchronization errors to zero in the form of a linear matrix inequality (LMI)-based feasibility problem, which can be efficiently solved using available tools. We illustrate the flexibility offered by a parameter-varying graph Laplacian formulation through two numerical examples that show the ability of the corresponding gain-scheduled consensus protocol to modulate various collective behaviors.