A　protocol　to　generate　steady　Knill–Laflamme–Milburn　(KLM)　states　of　two　Rydberg　atoms　with　dissipation　and　Lyapunov　control　is　proposed.　Herein,　combining　with　the　quantum　Zeno　dynamics　and　the　Rydberg　antiblockade,　a　unique　and　steady　solution　of　the　master　equation　of　the　system　is　obtained,　which　satisfies　the　definition　of　KLM　states.　Furthermore,　to　polish　the　convergence　rate,　well-designed　additional　coherent　control　(ACC)　fields　with　Lyapunov　control　are　added　into　the　traditional　dissipation　process.　Numerical　simulation　reveals　that　the　steady　target　state　generation　is　prominently　accelerated　and　the　protocol　is　robust　against　the　stochastic　noise　errors　caused　by　laser　fields.　It　is　hoped　that　the　work　may　provide　an　alternative　protocol　to　polish　the　generation　of　entanglement.　©　2019　WILEY-VCH　Verlag　GmbH　&　Co.　KGaA,　Weinheim