Consensus of Linear Multi-Agent System with Unknown Input Time-Varying Delay by Linear Time-Varying Protocol

This paper addresses the leader-following consensus problem of linear multi-agent systems subject to unknown input time-varying delays. A linear time-varying control protocol is proposed based on the parametric Lyapunov equation (PLE), and all parameters can be computed offline. By exploiting the properties of the PLE, it is proven that the proposed method ensures asymptotic leader-following consensus without requiring any a priori information on the delay value or its upper and lower bounds. Simulation results are provided to validate the theoretical analysis and demonstrate the effect of the design parameter on the system performance under unknown input time-varying delays.