An　autonomous　two-species　lolling-II　type　cooperative　system　with　single　feedback　control　is　considered　in　this　paper.　Firstly,　by　applying　the　comparison　theorem　of　differential　equation,　sufficient　conditions　which　ensure　the　permanence　of　the　system　are　obtained.　Secondly,　by　constructing　some　suitable　Lyapunov　function　and　using　the　average　Inequality,　some　sufficient　conditions　for　the　globally　asymptotical　stability　and　extinction　of　the　system　are　obtained.　Our　results　show　that　by　choosing　suitable　values　of　feedback　control　variables,　stable　species　could　become　extinct,　or　still　keep　the　property　of　globally　stable.　(C)　2015　Elsevier　Inc.　All　rights　reserved.