Direct　current　(DC)　microgrid　consists　of　many　parallel　power　converters　that　share　load　currents　through　the　inductance　of　DC/DC　converters.　Usually,　the　inductance　parameters　are　dependent　on　the　physical　implementation　of　the　system,　and　their　values　may　not　match　their　nameplates.　Such　disparities　could　lead　to　unequal　response　characteristics　of　the　system,　which　can　potentially　reduce　the　performances　of　the　DC　microgrid　operation.　This　paper　proposes　a　robust　control　strategy　for　inductive　parametric　uncertainties　of　DC/DC　converters　using　an　optimal　control　method　with　integral　action.　To　achieve　such　a　goal,　the　system　model　parameters　with　nominal　values　are　transformed　into　parametric　unmatched　uncertainties　to　form　a　robust　control　problem,　which　is　then　transformed　into　a　linear　quadratic　regulator　problem.　The　inductance　uncertainties　are　stabilized　with　the　uncertainty　dynamic　algebraic　Riccati　equation　(UDARE)　using　state　feedback　gain　under　linear　quadratic　regulator.　The　closed-loop　control　with　integral　action　is　adopted　to　achieve　a　steady-state　error　of　zero　on　the　DC-link　voltage　at　any　uncertainty　of　the　inductive　parameter,　which　subsequently　ensures　the　equal　load　current　sharing.　Off-line　simulations　and　real-time　validations　based　on　OpalRT　have　been　conducted　to　demonstrate　the　effectiveness　and　robustness　of　the　proposed　robust　control　strategy.