Uniform global position feedback tracking control of mechanical systems without friction

We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called Paden-Panja controller [20] where unavailable generalized velocities are replaced by approximate differentiation (dirty derivatives). The controller has been reported previously however, only semiglobal asymptotic stability has been established so far. The novelty of this paper relies in establishing a global property as well as in the method of proof, which does not follow Lyapunov's. However, the problem of finding a strict control Lyapunov function remains open.