Consensus of networked mechanical systems with time delays: A unified framework

In this paper, we address the consensus problem of networked uncertain mechanical systems on directed graphs containing a spanning tree. The challenge lies in the unclear input-output property of a strictly proper system transfer function involving time delays and the unclear limit value of a delay-dependent biproper transfer function. We establish a new input-output property of the delay-dependent strictly proper transfer function and moreover, via a constructive approach in frequency domain, we obtain the limit value of the biproper transfer function, upon which, we establish a unified framework to resolve the consensus problem of multiple mechanical systems. The proposed consensus framework unifies/extends the existing results and in addition gives rise to a fully cascade closed-loop system. With Lyapunov-like analysis and frequency domain input-output analysis, we demonstrate that the proposed unified consensus control framework ensures consensus without the integral action of the sliding vector, and scaled weighted average consensus with the integral action of the sliding vector. Simulation results are provided to demonstrate the performance of the proposed consensus schemes.