The　selection　of　weight　matrices　in　linear　quadratic　optimal　control　needs　a　lot　of　experience　and　skills.　Therefore,　a　question　relating　to　this　selection　is　studied,　which　is　whether　the　performance　function　(weight　matrix)　of　a　optimal　control　law　is　unique.　No　matter　in　single　input　case　or　multi　input　case,　many　performance　functions　lead　to　the　same　optimal　control　law　when　the　controllable　index　of　system　is　more　than　or　equal　to　2　and　the　diagonal　elements　of　the　weight　matrix　relating　to　this　control　input　have　two　no　zero　elements.