Boundary Control Design for a Flexible Manipulator with Input Backlash * *This work was supported by the National Basic Research Program of China (973 Program) under Grant 2013CB733100, the National Natural Science Foundation of China under Grant 61522302, 6161101273, the Newton Advanced Fellowship from The Royal Society, UK, under Grant NA160436 the Beijing Natural Science Foundation under Grant 4172041, and the Fundamental Research Funds for the China Central Universities of USTB under Grant FRF-BD-16-005A and FRF-TP-15-005C1.