This paper aims to investigate the consensus control of generic linear multi-agent systems (MASs) under directed dynamic topology. Nonnegative matrix theory, in particular the product properties of infinite row-stochastic matrices, which are widely used for multiple integrator agents, is explored to deal with the convergence analysis of generic linear MASs. It is finally shown that the exponential consensus can be reached under very relaxed conditions, i.e., the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough. Moreover, a least convergence rate and a bound for the unstable mode of the individual agent system, both of which are independent of the switching mode, can be explicitly specified. (C) 2014 Elsevier Ltd. All rights reserved.