The control of non-minimum phase systems remains an important open problem in nonlinear control, finding relevance in the control of underactuated and flexible systems. One wishes to cause the output of a dynamical system to track a desired trajectory while maintaining internal stability of a nominally unstable system. In this regard, motion control of structurally flexible robotic manipulators has drawn the attention of robotics researchers in the past few years. These robots find applications in space, underwater, and high speed energy efficient manipulation.

This dissertation aims to address two important issues regarding flexible link manipulators:​ Control design, and structural shape design. In this regard, two control strategies are considered. The first one is based on the concept of integral manifolds in singular perturbation theory, and the second is based on input-output decoupling in nonlinear systems theory. The practical implementation issues for the former require the inconvenient measurement of flexural rates. An observation strategy is proposed to circumvent this problem. Experimental evaluation of the control strategies are carried out on a setup constructed in the laboratory.

Furthermore, structural shape optimization is considered as a means to improve the dynamic behavior. In this regard, an optimization index is introduced to achieve some desired features such as higher flexible mode natural frequencies and easier accessibility of flexible modes by the control inputs.