Seeking Velocity-Free Consensus for Multi-Agent Systems With Nonuniform Communication and Measurement Delays

This paper addresses the consensus control problem of nonuniform delayed multi-agent systems without velocity measurements, and further obtains an explicit expression for the delay margin condition (critical time delay). Firstly, the passivity-based control technique is introduced to design the nominal consensus controller, which can enhance the robustness of the system by injecting additional relative damping. Then, the system states and the virtual state of the damping term are incrementally generalized into a third-order equation. Based on the frequency domain method, this equation was transformed into a high-order polynomial. Thus, the consensus conditions of the delayed multi-agent system are obtained according to the monotonicity of the polynomial. In detail, the conditions are presented in the form of an upper bound on the time delays and inequality sets of controller parameters. Finally, the effectiveness of the proposed controller and its corresponding consensus conditions are verified by designing the numerical simulation experiments.