This　work　investigates　the　time-varying　formation　tracking　(TVFT)　problem　for　linear　multi-agent　systems　with　a　leader　of　unknown　input　in　the　presence　of　unknown　external　disturbances　on　directed　graphs.　Each　agent　is　subjected　to　different　external　disturbances　generated　by　unknown　exosystems.　To　eliminate　the　unknown　external　disturbances　of　each　follower,　an　adaptive　disturbance　observer　and　a　state　observer　are　constructed　first.　Then,　utilizing　the　estimated　information,　a　fully　distributed　TVFT　protocol　is　designed　with　adaptive　coupling　parameters　such　that　the　global　information　of　the　communication　topology　is　not　required.　By　the　developed　distributed　controller,　the　multi-agent　system　on　a　communication　topology　containing　a　directed　spanning　tree　can　asymptotically　track　the　leader　with　a　desired　time-varying　formation　and　simultaneously　reject　external　disturbances　in　spite　of　their　unknown　exosystems.　Furthermore,　the　proposed　controller　is　modified　to　a　continuous　one　to　eliminate　the　chattering　problem.　Finally,　a　simulation　example　is　provided　to　illustrate　the　effectiveness　of　theoretical　results.　©　2024　International　Society　of　Automation