This　paper　discusses　the　leader-following　consensus　problem　of　second-order　homogeneous　multi-agents　systems,　in　which　it　takes　into　consideration　some　different　cases　about　the　parameter　in　position　difference　and　velocity　difference.　Firstly,　we　use　the　incidence　matrix　of　the　directed　spanning　tree　to　construct　a　linear　transformation　matrix,　and　the　consensus　problem　is　equivalently　converted　into　the　stability　problem　concerning　input　to　the　state.When　there　are　no　constraint　on　the　control　parameters,　through　Lyapunov　stability　and　the　linear　matrix　inequality,　we　can　get　better　control　parameters　to　make　the　system　asymptotically　reach　the　state　consensus　and　ensure　the　convergence　rate　of　the　system.　We　analyzed　three　special　cases　and　compared　the　previous　results.　We　use　the　condition　that　the　real　part　of　the　eigenvalue　of　matrix　equivalent　to　A　is　less　than　zero　when　the　matrix　is　Hurwitz　stable.　This　way　can　calculate　a　broader　set　of　values　of　the　control　parameters　more　simply　and　clearly.　Finally,　numerical　examples　are　presented　to　validate　the　theoretical　results.