Flexible robots are becoming more and more common in practical applications. This type of robots is characterized by the use of lightweight materials, which allows reducing their size, their power consumption and improves their safety. However, an accurate trajectory tracking of these systems is difficult to achieve because of the transient vibrations they undergo. This PhD thesis work is particularly devoted to the position control of flexible robotic manipulators at the joint and end-effector levels. Advanced control methods, based on some tools of the robust control theory and convex optimization, have been proposed. These methods are based on the theory of Linear Parameter Varying (LPV) systems and Linear Matrix Inequalities (LMI). Compared to some nonlinear control laws available in the literature that involve model inversion, theproposed LPV control laws make it possible to consider performance and robustness constraints in a simple and systematic manner. Our work particularly emphasizes on the appropriate management of the parametric dependence of the LPV model, especially the polynomial and rational dependences. Numerical simulations carried out in realistic operating conditions have shown a better robustness of the LPV control compared to the inversion-based nonlinear control withrespect to measurement noise, high frequency inputs and model uncertainties.
