Orbital feedback linearization of multi-input control affine systems

Feedback linearization is an effective design and analysis tool used in the study of nonlinear control systems. However cases arise where linearizability conditions cannot be met. For systems that are not linearizable by classical techniques, orbital feedback linearization (or feedback linearization by state-dependent time scaling) has been proposed to relax these conditions. In this paper, necessary and sufficient conditions for orbital feedback linearizability is presented for a class of multi-input nonlinear systems. The conditions axe simple and can be checked directly from the data of the problem. Using an exterior calculus approach, a simple algorithm is developed to compute state-dependent time scaling that yield state-feedback linearizable systems.