Consensus　analysis　and　design　problem　for　leader-following　linear　multi-agent　systems　(LLMASs)　with　directed　information　topology　was　investigated.　A　proper　linear　transformation　was　proposed　to　transform　the　consensus　problem　of　a　leader　with　disturbance　inputs　to　the　input-to-state　stability　problem　of　a　corresponding　linear　system.　Then,　a　new　consensus　criterion　in　terms　of　Hurwitz　stability　of　matrices　was　given　for　LLMASs　achieving　consensus　with　directed　information　topologies,　and　the　tracking　error　was　estimated.　Moreover,　a　design　process　to　determine　the　feedback　gain　matrix　in　the　consensus　protocol　was　proposed.　Finally,　the　consensus　was　extended　to　the　formation　control.　Numerical　examples　are　given　to　validate　the　above　theoretical　results.　©　2017,　Central　South　University　Press.　All　right　reserved.