This　article　investigates　a　robust　variable　impedance　control　methodology　for　aerial　manipulators　to　realize　compliant　and　safe　interaction　tasks.　Considering　that　the　stability　characteristics　are　generally　overlooked　in　existing　variable　impedance　controllers　of　the　aerial　manipulator,　state-independent　stability　conditions　are　applied　for　time-varying　impedance　profiles　to　ensure　the　exponential　stability　of　the　desired　variable　impedance　dynamics　(DVID)　as　well　as　the　boundedness　of　the　state　variables　in　the　DVID.　A　command　trajectory　variable　is　introduced　for　converting　the　impedance　control　issue　to　a　particular　tracking　issue,　and　then,　a　robust　variable　impedance　controller　based　on　the　wrench　estimator　is　designed　to　guarantee　the　exponential　convergence　of　the　translational　states　and　impedance　error　of　the　aerial　manipulator.　The　designed　impedance　controller　is　structurally　simple　and　results　in　low　implementation　costs.　Next,　an　improved　attitude　control　approach　with　the　command　filter　is　developed　for　global　flight　attitude　stability　without　any　singularities　or　ambiguities,　where　the　filter　is　introduced　to　avoid　computing　the　derivative　signals　of　the　generalized　force　input.　Finally,　the　effectiveness　of　the　proposed　control　method　is　illustrated　via　numerical　simulations　and　interaction　experiments　with　different　targets　in　real　scenarios.