This paper focuses on analyzing the finite-time convergence of a nonlinearconsensus algorithm for multi-agent networks with unknown inherent nonlineardynamics. Due to the existence of the unknown inherent nonlinear dynamics, thestability analysis and the finite-time convergence analysis of the closed-loopsystem under the proposed consensus algorithm are more challenging than thoseunder the well-studied consensus algorithms for known linear systems. For thispurpose, we propose a novel stability tool based on a generalized comparisonlemma. With the aid of the novel stability tool, it is shown that the proposednonlinear consensus algorithm can guarantee finite-time convergence if thedirected switching interaction graph has a directed spanning tree at each timeinterval. Specifically, the finite-time convergence is shown by comparing theclosed-loop system under the proposed consensus algorithm with somewell-designed closed-loop system whose stability properties are easier toobtain. Moreover, the stability and the finite-time convergence of theclosed-loop system using the proposed consensus algorithm under a (general)directed switching interaction graph can even be guaranteed by the stabilityand the finite-time convergence of some special well-designed nonlinearclosed-loop system under some special directed switching interaction graph,where each agent has at most one neighbor whose state is either the maximum ofthose states that are smaller than its own state or the minimum of those statesthat are larger than its own state. This provides a stimulating example for thepotential applications of the proposed novel stability tool in the stabilityanalysis of linear/nonlinear closed-loop systems by making use of known resultsin linear/nonlinear systems. For illustration of the theoretical result, weprovide a simulation example.
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