This　paper　focuses　on　the　leader-following　consensus　problem　of　multi-agent　systems　under　both　undirected　and　directed　networks,　where　each　agent　is　subject　to　the　switched　linear　dynamics.　It　is　assumed　that　the　switching　between　the　subsystems　of　the　agents　is　arbitrary.　We　utilize　the　incidence　matrix　of　a　virtual　directed　spanning　tree　rooted　at　the　leader　to　construct　a　linear　transformation　matrix　so　as　to　equivalently　transform　the　leader-following　consensus　problem　into　the　globally　uniformly　asymptotic　stability　(GUAS)　problem　of　a　switched　linear　system.　Then,　based　on　the　common　Lyapunov　function　method,　we　derive　some　sufficient　conditions　in　terms　of　the　linear　matrix　inequalities　(LMIs)　to　assure　the　globally　uniformly　asymptotic　consensus　of　the　multi-agent　system.　Finally,　some　numerical　examples　are　given　to　illustrate　the　effectiveness　of　the　theoretical　results.　©　2021　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.