Designing an LMI-Based Robust Leader-Following Consensus Control for Time-Delayed Multi-Agent Systems with Unknown Coefficient Matrix

In this paper, a robust controller is designed for a multi-agent system comprising a leader agent and  followers. Follower agents are supposed to have linear dynamics with time-delay considering uncertainties in state- space coefficient matrices. The dynamics of the leader agent are similar to the followers; however, without any uncertainty. The purpose of the consensus controller is to make the follower agent state variables to track the leader in presence of time-delay and uncertainties. The necessary condition for consensus is the existence of at least a spanning tree in the graph corresponding to a multi-agent system. If the condition is met, a feedback linearization controller is firstly designed for the leader to reach the desired position; then a  robust controller is proposed for each follower to eliminate the effect of model uncertainties by defining the consensus error dynamic between the followers and leader and assuming a specific amount of delay for all agents. High precision, fast convergence, and good robustness against uncertainties are ensuredthanks to the newly proposed control scheme. Finally, asymptotic convergence of the consensus error to zero is guaranteed and LMI conditions for the stability of the closed-loop system is presented. Simulation results show the stability and effectiveness of the proposed controller.