Homogeneous continuous finite-time observer for the triple integrator

In this paper we consider the continuous homogeneous observer defined in [1] in the case of the triple integrator. In [1], convergence of the algorithm was only proved when the degree of homogeneity was sufficiently close to 0 without more tractable information. We show here that, in the case of the triple integrator, the observer presents global finite-time stability for any negative degree under constructive conditions on the gains. This is achieved with a homogeneous Lyapunov function design. Simulations of the proposed observer are also provided.