Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework

This technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays. The challenge lies in the unclear input-output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input. We establish a new input-output property of this linear networked system and moreover its convergent property under an external input, 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 yields a fully cascaded closed-loop system. With Lyapunov-like analysis and frequency domain input-output analysis, we show that the proposed unified consensus control scheme 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.