Transformation Synthesis for Euler-Lagrange Systems
Résumé
The transformation of Euler-Lagrange systems, with the variable of position as output, in order to solve some interesting problem as the design of observer is considered in this paper. First, we will provide a necessary and sufficient condition, which ensures the transformation of such system into some structure affine in the velocities, as well as a method to compute this transformation. For a particular family of Euler-lagrange systems with two degree of freedom we will present a change of coordinates which makes the dynamics triangular with respect to the velocities and a globally asymptotically converging observer is provided. To illustrate the approach, it is applied to the Cart-pendulum system.