This　paper　presents　an　analytical　investigation　into　active　vibration　control　of　flexible　redundant　robot　manipulators　featuring　piezoelectric　actuators　and　strain　gage　sensors.　The　state-space　expression　of　the　discrete　time-varying　dynamic　system　is　developed　firstly.　The　LQR　optimal　control　law　is　presented　based　upon　the　discrete　Minimum　Principle.　Moreover,　an　approximate　method　is　proposed　for　estimating　the　state　information　of　the　system.　Finally,　a　planar　3R　flexible　redundant　manipulator　is　utilized　as　an　illustration　example.　The　simulation　results　show　that　the　dynamic　performance　of　the　manipulator　has　been　improved　significantly.