On the construction of static stabilizers and static output trackers for dynamically linearizable systems, related results and applications

It is shown that the property of dynamic linearizability, to be understood as linearizability by means of the dynamic extension algorithm, implies the existence of static, possibly time varying, control laws yielding asymptotic output tracking with arbitrary speed of convergence and asymptotic stabilization with a computable bound on the region of attraction. Similar results hold for systems which are only input/output linearizable by means of dynamic state feedback, provided that the inverse dynamics possess certain stability properties. Applications of these results to the problem of regional stabilization of a VTOL aircraft is considered, together with the tracking problem for a class of flexible joints robots. Moreover, a novel parameterization for flexible joint robots is also proposed.