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We consider finite and infinite-dimensional first-order consensus systemswith timeconstant interaction coefficients. For symmetric coefficients,convergence to consensus is classically established by proving, for instance,that the usual variance is an exponentially decreasing Lyapunov function. Weinvestigate here the convergence to consensus in the non-symmetric case: weidentify a positive weight which allows to define a weighted mean correspondingto the consensus, and obtain exponential convergence towards consensus.Moreover, we compute the sharp exponential decay rate.

Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions