Orbital feedback linearization for multi-input control systems

Abstract

A nonlinear control system is said to be orbital feedback linearizable if there exist an invertible static feedback and a change of time scale (depending on the state) which transform the system into a linear system. We give geometric necessary and sufficient conditions describing multi-input control-affine systems that are orbital feedback linearizable out of equilibria and in the case of equal controllability indices. We also describe a construction of the time rescaling needed to orbitally linearize the system. Moreover, we analyze close relations between orbital feedback linearizable control-affine systems and control-linear systems that are feedback equivalent to a multi-chained form comparing geometric structures corresponding to both problems. We illustrate our results by two examples, one being a rigid bar moving in R3.