Using　a　linear　Kalman　filter　approach(LKFA),　this　study　proposes　sensor-less　finite-control-set　model　predictive　control　for　stabilizing　DC-grid　voltage　estimation　in　direct　current　microgrids　(DCMs).　In　controlling　many　parallel　power　converters　in　DCMs,　the　proposed　control　method　eliminates　the　need　for　an　inductance　current　sensor.　The　second　prediction　is　derived　from　the　state-space　model　so　that　an　efficient　algorithm　may　be　performed.　The　dynamic　model　of　DCMs　in　the　second　prediction　is　converted　into　a　stationary　linear　stochastic　discrete　time-invariant　system　to　standardize　the　state　estimation　design.　The　DC-grid　voltage　reference　is　then　computed　adopting　LKFA　using　a　state　feedback　control　law　based　on　the　dynamic　algebraic　Riccati　equation　with　integral　action　to　guarantee　zero　steady-state　error　during　transient　responses.　Under　load　demand　variation,　the　efficacy　of　the　proposed　approach　is　shown　using　a　sensor-less　control　algorithm.　Robustness　against　parametric　uncertainty,　DC-grid　voltage　estimation,　and　equally　estimated　power-sharing　amongst　DERs　have　all　been　achieved,　as　have　the　fast　convergence.　©　2021　IEEE.