In　this　paper,　we　propose　a　scheme　for　speeding　up　the　generation　of　steady-state　entanglement　of　two　interacting　qubits　by　coupling　them　with　an　engineered　dissipative　ancilla.　The　coupling　strength　between　the　target　qubits　and　the　ancilla　is　tailored　by　state-based　Lyapunov　control,　which　vanishes　gradually　along　with　the　increasing　of　the　fidelity　of　steady　state.　The　negativity　is　adopted　to　measure　the　bipartite　entanglement,　which　would　not　be　enhanced　by　such　Lyapunov　control.　In　order　to　speed　up　and　enhance　the　bipartite　entanglement,　we　further　use　the　non-vanishing　engineered　coupling.　Numerical　simulations　indicate　that　the　scheme　is　robust　against　the　fluctuations　of　the　coupling　strength　and　immune　to　the　system　parametric　errors.　The　study　shows　promising　performance　of　speeding　up　dissipative　generation　of　quantum　states　with　Lyapunov　control.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.