A　scheme　to　implement　the　controlled-NOT　(CNOT)　gate　for　quantum　systems　is　proposed,　which　is　based　on　Lyapunov　control.　The　scheme　does　not　require　precise　control　of　the　interaction　time　since　the　system　is　stable　when　the　control　fields　vanish.　In　particular,　the　control　fields　can　be　easily　obtained　by　most　initial　states.　As　an　example,　the　CNOT　gate　is　realized　for　two　atoms　trapped　in　an　optical　cavity　by　exploiting　two　disturbance　cases.　Compared　to　continuous　disturbance,　the　fidelity　of　the　CNOT　gate　is　higher　under　impulsive　disturbance,　however,　interaction　times　are　much　longer.　Numerical　simulations　indicate　that　the　scheme　is　robust　against　variations　of　control　parameters　and　decoherence　caused　by　atomic　spontaneous　emission　and　cavity　decay.　Therefore,　the　scheme　may　provide　useful　applications　in　quantum computation.　©　2019　WILEY-VCH　Verlag　GmbH　&　Co.　KGaA,　Weinheim