Average Consensus of Multi-agent Systems with Time Delay Using Packet Selection Considering Nth-order Compensation

 This study proposes a stabilization approach when applying $N$th-order compensation for the average consensus of a multi-agent system affected by non-uniform, asymmetric, and time-varying delays in a communication network.A continuous-time linear dynamical system with a local discrete-time controller modeled for each agent.In our previous study, we proposed a packet selection algorithm that always selects the most recent packet and a synchronization algorithm that compensates for asymmetric delays to achieve an average consensus considering first-order compensation.In Addition, we proved sufficient conditions for the stability of the average consensus with these two algorithms, which are applied when the maximum delay is known, based on the Lyapunov theory using linear matrix inequalities (LMIs).In this study, we extend this method to handle Nth-order compensation.First, an extended packet selection algorithm is investigated using a simulation.Next, we propose a Lyapunov function with $N$th-order compensation and prove sufficient conditions for stability via linear matrix inequalities (LMIs).Finally, we evaluated the effectiveness of the proposed Lyapunov function using a numerical simulation.