Consensus of nonlinear multi-agent systems with self and communication time delays: A unified framework

In this paper, we study the consensus problem of multi-agent systems with parametric uncertainties on directed graph communication topologies containing a spanning tree. The challenge lies in that the input-output property of a strictly proper system transfer function involving self and communication delays and the extremum of a delay-involved transfer function are both unclear. By establishing a new input-output property of the delay-involved strictly proper transfer function and applying a constructive approach in frequency domain, we obtain the extremum of the delay-involved transfer function, upon which, we establish a unified framework to resolve the consensus problem of multi-agent systems with parametric uncertainties and time delays, and the terminal convergence point value is achieved. Based upon Lyapunov stability theory and frequency domain input-output analysis, we demonstrate that the proposed unified consensus control framework ensures scaled weighted average consensus with the integral action of the synchronization signal vector. Simulation results are provided to demonstrate the effectiveness of the proposed consensus scheme.